Graph Linear and Quadratic Functions: CCSS.Math.Content.HSF-IF.C.7a - Common Core: High School - Functions

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is three.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative one.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is five.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is four.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is one.

Step 3: Answer the question.

The -intercept is one.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the maximum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is three.

Step 3: Answer the question.

The -intercept is three.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is zero.

Step 3: Answer the question.

The -intercept is zero.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is two.

Step 3: Answer the question.

The -intercept is two.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

Therefore the -intercept lies at the point which means the -intercept is four.

Step 3: Answer the question.

The -intercept is four.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the parabola is shifted to the right therefore the -intercept of the graph is not at the vertex.

Therefore the -intercept lies at the point which means the -intercept is one.

Step 3: Answer the question.

The -intercept is one.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is three.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative one.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is five.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is four.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a linear function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a straight line, the general algebraic form of the function is,

where

Step 2: Identify where the graph crosses the -axis.

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the minimum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is one.

Step 3: Answer the question.

The -intercept is one.

This question tests one's ability to recognize algebraic characteristics of a graph. This particular question examines a quadratic function.

For the purpose of Common Core Standards, "graph linear and quadratic functions and show intercepts, maxima, and minima" falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.7).

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 the general algebraic function for the given graph.

Since the graph is that of a parabola opening up, the general algebraic form of the function is,

where

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if then the width of the parabola is wider; if then the parabola is narrower.

Step 2: Identify where the graph crosses the -axis.

For the function above, the vertex is also the maximum of the function and lies at the -intercept of the graph.

Therefore the vertex lies at which means the -intercept is three.

Step 3: Answer the question.

The -intercept is three.