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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 #71 : Interpreting Functions

Screen shot 2016 01 12 at 2.32.17 pm

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

$\textup{y-intercept}=1.5$ $\displaystyle \textup{y-intercept}=1.5$

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 12 at 2.32.17 pm

Therefore the general form of the function looks like,

y=mx+3 $\displaystyle y=mx+3$

Step 3: Answer the question.

The $\displaystyle y$ -intercept is three.

Report an Error

Example Question #72 : Interpreting Functions

Screen shot 2016 01 22 at 2.07.51 pm

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

$\textup{y-intercept}=0$ $\displaystyle \textup{y-intercept}=0$

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

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

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 22 at 2.07.51 pm

Therefore the general form of the function looks like,

y=mx-1 $\displaystyle y=mx-1$

Step 3: Answer the question.

The $\displaystyle y$ -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 $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 22 at 2.04.50 pm

Therefore the general form of the function looks like,

y=mx+5 $\displaystyle y=mx+5$

Step 3: Answer the question.

The $\displaystyle y$ -intercept is five.

Report an Error

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

Screen shot 2016 01 22 at 2.04.27 pm

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 22 at 2.04.27 pm

Therefore the general form of the function looks like,

y=mx-2 $\displaystyle y=mx-2$

Step 3: Answer the question.

The $\displaystyle y$ -intercept is negative two.

Report an Error

Example Question #73 : Interpreting Functions

Screen shot 2016 01 22 at 2.04.01 pm

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 22 at 2.04.01 pm

Therefore the general form of the function looks like,

y=mx+4 $\displaystyle y=mx+4$

Step 3: Answer the question.

The $\displaystyle y$ -intercept is four.

Report an Error

Example Question #74 : Interpreting Functions

Screen shot 2016 01 22 at 2.03.07 pm

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

$\textup{y-intercept}=0$ $\displaystyle \textup{y-intercept}=0$

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

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

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

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

Correct answer:

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

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 $\displaystyle y=mx+b$

where

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -axis.

Screen shot 2016 01 22 at 2.03.07 pm

Therefore the general form of the function looks like,

y=mx-2 $\displaystyle y=mx-2$

Step 3: Answer the question.

The $\displaystyle y$ -intercept is negative two.

Report an Error

Example Question #75 : Interpreting Functions

Screen shot 2016 01 23 at 7.48.31 am

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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,

$\displaystyle y=ax^2+bx+c$

where

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

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

Step 2: Identify where the graph crosses the $\displaystyle y$ -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 $\displaystyle y$ -intercept of the graph.

c=1 $\displaystyle c=1$

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

Step 3: Answer the question.

The $\displaystyle y$ -intercept is one.

Report an Error

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

Screen shot 2016 01 23 at 7.49.00 am

What is the $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

$\textup{y-intercept}=0$ $\displaystyle \textup{y-intercept}=0$

Correct answer:

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

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,

$\displaystyle y=ax^2+bx+c$

where

Step 2: Identify where the graph crosses the $\displaystyle y$ -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 $\displaystyle y$ -intercept of the graph.

c=3 $\displaystyle c=3$

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

Step 3: Answer the question.

The $\displaystyle y$ -intercept is three.

Report an Error

Example Question #2 : 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 $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

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

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

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

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

Correct answer:

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

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,

$\displaystyle y=ax^2+bx+c$

where

Step 2: Identify where the graph crosses the $\displaystyle y$ -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 $\displaystyle y$ -intercept of the graph.

c=2 $\displaystyle c=2$

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

Step 3: Answer the question.

The $\displaystyle y$ -intercept is two.

Report an Error

Example Question #2 : 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 $\displaystyle y$ -intercept of the function that is depicted in the graph above?

Possible Answers:

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

$\textup{y-intercept}=0$ $\displaystyle \textup{y-intercept}=0$

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

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

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

Correct answer:

$\textup{y-intercept}=0$ $\displaystyle \textup{y-intercept}=0$

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,

$\displaystyle y=ax^2+bx+c$

where

Step 2: Identify where the graph crosses the $\displaystyle y$ -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 $\displaystyle y$ -intercept of the graph.

c=0 $\displaystyle c=0$

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

Step 3: Answer the question.

The $\displaystyle y$ -intercept is zero.

Report an Error

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All Common Core: High School - Functions Resources

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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 #71 : Interpreting Functions

Example Question #72 : Interpreting Functions

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 #73 : Interpreting Functions

Example Question #74 : Interpreting Functions

Example Question #75 : Interpreting Functions

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

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

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

All Common Core: High School - Functions Resources

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