Building Functions - Common Core: High School - Functions
Card 0 of 432
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function 
results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to 
which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
The inverse graphed alone is as follows.
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
The inverse graphed alone is as follows.
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically
.
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
.
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
What is the inverse of the following function?
What is the inverse of the following function?
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function results in the following graph.
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to which results in the following graph.
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
This question is testing ones ability to understand what it means for a function to be invertible or non-invertible and how to find the inverse of a non-invertible function through means of domain restriction.
For the purpose of Common Core Standards, "Produce an invertible function from a non-invertible function by restricting the domain." falls within the Cluster B of "Build new functions from existing functions" concept (CCSS.MATH.CONTENT.HSF-BF.B.4d). It is important to note that this standard is not directly tested on but, it is used for building a deeper understanding on invertible and non-invertible functions and their inverses.
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Determine whether the function given is invertible or non-invertible.
Using technology to graph the function
This function is non-invertible because when taking the inverse, the graph will become a parabola opening to the right which is not a function. A sideways opening parabola contains two outputs for every input which by definition, is not a function.
Step 2: Make the function invertible by restricting the domain.
To make the given function an invertible function, restrict the domain to
Step 3: Graph the inverse of the invertible function.
Swapping the coordinate pairs of the given graph results in the inverse.
Therefore, the inverse of this function algebraically is
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every 
days and can be modeled by a function 
which depends on 
days. Before the fertilizer is added to the pot, Janet had two blooms. Write a function that models the number of blooms in 
days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every 
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer produces four blooms every two days. If 
is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer produces four blooms every two days. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had three blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is three.
The fertilizer produces four blooms every two days. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.MATH.CONTENT.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is three.
The fertilizer produces four blooms every two days. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had one bloom. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every two days and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is one.
The fertilizer produces four blooms every two days. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is one.
The fertilizer produces four blooms every two days. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every 
days and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had seven blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms quadruples every 
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is seven.
The fertilizer produces four blooms every two days. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is seven.
The fertilizer produces four blooms every two days. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is four every two days. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had three blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is three.
The fertilizer doubles the blooms every day. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is three.
The fertilizer doubles the blooms every day. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had two blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer doubles the blooms every day. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer doubles the blooms every day. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had five blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms doubles every day and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is five.
The fertilizer doubles the blooms every day. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is five.
The fertilizer doubles the blooms every day. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is two every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms triple every day and can be modeled by a function which depends on days. Before the fertilizer is added to the pot, Janet had two blooms. Write a function that models the number of blooms in days since the fertilizer was added.
Janet is fertilizing her flowers with a special mixture. Once the mixture is added to the flower pot the flower's blooms triple every day and can be modeled by a function
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer triples the blooms every day. If is representing days then the rate of the blooms is,
.
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is three every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
This particular question is testing one's ability to combine standard functions using arithmetic operations given a real world type of problem. This type of problem tests the ability to identify relationships and form a mathematical model to describe said relationship.
For the purpose of Common Core Standards, combining standard functions using arithmetic operations falls within the Cluster A of build a function that models a relationship between two quantities concept (CCSS.Math.content.HSF.BF.A).
Knowing the standard and the concept for which it relates to, we can now do the step-by-step process to solve the problem in question.
Step 1: Identify what the question is asking for.
Step 2: Identify the information that is given in the question.
Step 3: Use algebraic methods to state mathematical relationships and produce function.
Using the steps outlined above is as follows.
Step 1: Identify what the question is asking for.
This question is asking to find the mathematical function that describes the effect the fertilizer has on the flower pot.
Step 2: Identify the information that is given in the question.
Initial amount of blooms prior to introducing the fertilizer is two.
The fertilizer triples the blooms every day. If
Notice that this question is talking about a growth rate therefore, we can use the following formula.
The number of blooms that form after the fertilizer is introduced is three every day. Therefore,
Step 3: Use algebraic methods to state the mathematical relationship and produce the function.
Using the information we found in Step 2 and substituting it into the general formula for growth, we can create the function that represents the effect that the fertilizer has on the flower pot's blooms. Thus arriving at the solution.
Compare your answer with the correct one above