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

Study concepts, example questions & explanations for Common Core: High School - Functions

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All Common Core: High School - Functions Resources

6 Diagnostic Tests 82 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

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Example Question #1 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 12 at 2.32.17 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 12 at 2.32.17 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is three.

Example Question #2 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 22 at 2.07.51 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 22 at 2.07.51 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative one.

Example Question #3 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 22 at 2.04.50 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 22 at 2.04.50 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is five.

 

Example Question #4 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 22 at 2.04.27 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 22 at 2.04.27 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

Example Question #2 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 22 at 2.04.01 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 22 at 2.04.01 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is four.

Example Question #3 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 22 at 2.03.07 pm

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 22 at 2.03.07 pm

Therefore the general form of the function looks like,

Step 3: Answer the question.

The -intercept is negative two.

Example Question #7 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 23 at 7.48.31 am

What is the -intercept of the function that is depicted in the graph above?

 

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 23 at 7.48.31 am

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.

Example Question #8 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 23 at 7.49.00 am

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 23 at 7.49.00 am

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.

Example Question #4 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 23 at 7.49.43 am

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 23 at 7.49.43 am

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.

Example Question #10 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

Screen shot 2016 01 23 at 7.49.20 am

What is the -intercept of the function that is depicted in the graph above?

Possible Answers:

Correct answer:

Explanation:

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.

Screen shot 2016 01 23 at 7.49.20 am

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.

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All Common Core: High School - Functions Resources

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