Linear, Quadratic, & Exponential Models* - Common Core: High School - Functions

Card 0 of 332

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=100(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=100(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=100(2^{24})^x \P_{hours}(24x)=100(16777216)^x \P_{days}(t)=100(16777216)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=46(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=46(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=46(2^{24})^x \P_{hours}(24x)=46(16777216)^x \P_{days}(t)=46(16777216)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=34(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=34(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=34(2^{24})^x \P_{hours}(24x)=34(16777216)^x \P_{days}(t)=34(16777216)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=34(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=34(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=34(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=34(1.012)^x \P_{minutes}(t)=34(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=49(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=49(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=49(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=49(1.012)^x \P_{minutes}(t)=49(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=12(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=12(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=12(2^{24})^x \P_{hours}(24x)=12(16777216)^x \P_{days}(t)=12(16777216)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=9(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=9(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=9(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=9(1.012)^x \P_{minutes}(t)=9(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=4(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=4(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=4(2^{24})^x \P_{hours}(24x)=4(16777216)^x \P_{days}(t)=4(16777216)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=14(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=14(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=14(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=14(1.012)^x \P_{minutes}(t)=14(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=68(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=68(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=68(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=68(1.012)^x \P_{minutes}(t)=68(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=168(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{minutes}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of minutes as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ hour}=60\textup{\ minutes}$

So if

$x=\textup{hour}$

then

$1\textup{ minute}=\frac{x}{60}$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=168(2^x)$

Let represent time in minutes

$P_{minutes}(t)=P_{minutes}\left(\frac{x}{60} \right )$

$\P_{minutes}\left(\frac{x}{60} \right )=168(2^{\frac{1}{60}})^x \\P_{minutes}\left(\frac{x}{60} \right )=168(1.012)^x \P_{minutes}(t)=168(1.012)^t$

Compare your answer with the correct one above

Question

Certain diseases, such as bovine spongiform encephalopathy (mad cow disease), are caused by prions - misfolded proteins. These prions are irreversibly misfolded and cause subsequent misfolding of healthy proteins when they come into contact with them. Joe ate the meat of a cow with BSE, ingesting prions, and each prion caused the misfolding of a new protein every number of hours, is illustrated by the following function.

$P_{hours}(x)=20(2^x)$

where $P_{hours}(x)$ is how many misfolded proteins are present after hours.

What is the function for $P_{days}(t)$ ?

Answer

This question tests one's ability to recognize real life situations where a quantity changes at a constant rate per an interval. It also builds on the concept of converting between units within a function. Questions like this, allow and encourage abstract reasoning and contextualizing.

For the purpose of Common Core Standards, recognizing situations where one quantity changes at a constant rate per interval relative to another, falls within the Cluster A of construct and compare linear, quadratic, and exponential model and solve problems concept (CCSS.Math.content.HSF.LE.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.

This particular question is asking for the function when is in terms of days as opposed to the given function which has in hours.

Step 2: Identify the conversion factor.

The conversion factor will be from hours to days.

$1\textup{ day}=24\textup{\ hours}$

So if

$x=\textup{hour}$

then

$1\textup{ day}=24x$

Step 3: Manipulate the original function to get new function.

Given the original function:

$P_{hours}(x)=20(2^x)$

Let represent time in days

$P_{days}(t)=P_{days}(24x)$

$\P_{hours}(24x)=20(2^{24})^x \P_{hours}(24x)=20(16777216)^x \P_{days}(t)=20(16777216)^t$

Compare your answer with the correct one above

Question

What is the function that describes the following graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The red lines in the below graph represent the slope.

The rise is three units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{5-2}{1-0}=\frac{3}{1}=3$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The red lines in the below graph represent the slope.

The rise is two units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2-0}{1-0}=\frac{2}{1}=2$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{0--1}{1-0}=\frac{1}{1}=1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is three units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{2--1}{1-0}=\frac{3}{1}=3$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=1$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is two units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{3-1}{1-0}=\frac{2}{1}=2$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is four units up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{4-0}{1-0}=\frac{4}{1}=4$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=0$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is two units to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{1-0}{2-0}=\frac{1}{2}$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

$y=\frac{1}{2}x$

Compare your answer with the correct one above

Question

What is the function that describes the graph?

Answer

This question is testing one's ability to identify and construct an algebraic function given a graph.

For the purpose of Common Core Standards, "Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table)." falls within the Cluster A of "Construct and compare linear, quadratic, and exponential models and solve problems" concept (CCSS.MATH.CONTENT.HSF-LE.A.2).

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 -intercept.

Recall that the -intercept is the point at which the line crosses the -axis. In other words, it is at the point where .

$\textup{y-intercept}=-2$

Step 2: Identify the slope.

Recall that slope is known as rise over run or the change in the y values over the change in x values.

$\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}$

The rise is one unit up and the run is one unit to the right.

$\textup{slope}=\frac{\textup{rise}}{\textup{run}}=\frac{\Delta y}{\Delta x}=\frac{y_2-y_1}{x_2-x_1}=\frac{-1--2}{1-0}=\frac{1}{1}=1$

Step 3: Construct the equation using the slope-intercept form of a linear function.

The slope-intercept form of a linear function is,

$\y=mx+b \m=\textup{Slope} \b=\textup{y-intercept}$ .

Substitute the slope and intercept into the general form to construct this particular function.

Compare your answer with the correct one above

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