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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

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:

$\textup{y-intercept}=3$

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

$\textup{y-intercept}=1$

$\textup{y-intercept}=1.5$

$\textup{y-intercept}=2$

Correct answer:

$\textup{y-intercept}=3$

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx+3

Step 3: Answer the question.

The -intercept is three.

Report an Error

Example Question #1 : 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:

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

$\textup{y-intercept}=1$

$\textup{y-intercept}=0$

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

$\textup{y-intercept}=-\frac{1}{2}$

Correct answer:

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

Explanation:

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

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx-1

Step 3: Answer the question.

The -intercept is negative one.

Report an Error

Example Question #1 : 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:

$\textup{y-intercept}=-5$

$\textup{y-intercept}=3$

$\textup{y-intercept}=5$

$\textup{y-intercept}=2$

$\textup{y-intercept}=1$

Correct answer:

$\textup{y-intercept}=5$

Explanation:

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

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx+5

Step 3: Answer the question.

The -intercept is five.

Report an Error

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:

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

$\textup{y-intercept}=3$

$\textup{y-intercept}=1$

$\textup{y-intercept}=2$

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

Correct answer:

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

Explanation:

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

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx-2

Step 3: Answer the question.

The -intercept is negative two.

Report an Error

Example Question #1 : 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:

$\textup{y-intercept}=2$

$\textup{y-intercept}=-8$

$\textup{y-intercept}=-4$

$\textup{y-intercept}=4$

$\textup{y-intercept}=3$

Correct answer:

$\textup{y-intercept}=4$

Explanation:

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

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx+4

Step 3: Answer the question.

The -intercept is four.

Report an Error

Example Question #6 : 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:

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

$\textup{y-intercept}=3$

$\textup{y-intercept}=2$

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

$\textup{y-intercept}=0$

Correct answer:

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

Explanation:

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

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,

y=mx+b

where

$\\m=\textup{slope} \\b=\textup{y-intercept}$

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,

y=mx-2

Step 3: Answer the question.

The -intercept is negative two.

Report an Error

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:

$\textup{y-intercept}=\frac{1}{2}$

$\textup{y-intercept}=1$

$\textup{y-intercept}=2$

$\textup{y-intercept}=-3$

$\textup{y-intercept}=3$

Correct answer:

$\textup{y-intercept}=1$

Explanation:

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

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,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 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.

c=1

Therefore the vertex lies at (0,1) which means the -intercept is one.

Step 3: Answer the question.

The -intercept is one.

Report an Error

Example Question #4 : 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:

$\textup{y-intercept}=1$

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

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

$\textup{y-intercept}=3$

$\textup{y-intercept}=0$

Correct answer:

$\textup{y-intercept}=3$

Explanation:

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

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,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 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.

c=3

Therefore the vertex lies at (0,3) which means the -intercept is three.

Step 3: Answer the question.

The -intercept is three.

Report an Error

Example Question #1 : 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:

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

$\textup{y-intercept}=3$

$\textup{y-intercept}=1$

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

$\textup{y-intercept}=2$

Correct answer:

$\textup{y-intercept}=2$

Explanation:

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

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,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 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.

c=2

Therefore the vertex lies at (0,2) which means the -intercept is two.

Step 3: Answer the question.

The -intercept is two.

Report an Error

Example Question #9 : 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:

$\textup{y-intercept}=1$

$\textup{y-intercept}=2$

$\textup{y-intercept}=0$

$\textup{y-intercept}=3$

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

Correct answer:

$\textup{y-intercept}=0$

Explanation:

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

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,

y=ax^2+bx+c

where

$\\a=\textup{The width/pitch of the parabola} \\b=\textup{Relates to the vertex}=\frac{-b}{2a} \\c=\textup{Vertical Shift}$

Recall that if is negative the parabola opens down and if is positive then the parabola opens up. Also, if 0<a<1 then the width of the parabola is wider; if a>1 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.

c=0

Therefore the vertex lies at (0,0) which means the -intercept is zero.

Step 3: Answer the question.

The -intercept is zero.

Report an Error

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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

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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

All Common Core: High School - Functions Resources

Example Questions

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

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

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

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

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

Example Question #6 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

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

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

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

Example Question #9 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

All Common Core: High School - Functions Resources

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