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Common Core: High School - Functions : Interpreting Functions

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

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Example Question #11 : Average Rate Of Change: Ccss.Math.Content.Hsf If.B.6

Diane, Jane, and Hector participated in a relay race. The following table shows the distance they each ran and the amount of time it took them.

$\begin{tabular}{ |c|c|c|c| } \hline & Miles& Time \\ \hline Diane & 3& 39 min. \\ Jane & 4&52 min.\\ Hector &5&65 min.\\ \hline \end{tabular}$

Who had the fastest pace?

Possible Answers:

$\text{All paces are the same.}$

$\text{Jane}$

$\text{Hector}$

$\text{Diane}$

$\text{More information is needed}$

Correct answer:

$\text{All paces are the same.}$

Explanation:

This question is testing one's ability interpret a table and identify the rate of change.

For the purpose of Common Core Standards, "calculate and interpret the average rate of change of a function over a specific interval" falls within the Cluster B of "interpret functions that arise in applications in terms of the context" concept (CCSS.MATH.CONTENT.HSF-IF.B.5).

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 average rate of change formula for calculations.

$\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

In the particular case, to find the fastest pace person, there will need to an average rate of change calculation done for each person to find their mile pace.

Step 2: Calculate the mile pace for Diane, Jane, and Hector.

$\textup{Diane's Pace: }P_D=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

$\textup{Jane's Pace: }P_J=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

$\textup{Hector's Pace: }P_H=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

Using the information provided by the table, calculate the pace of each individual.

$\begin{tabular}{ |c|c|c|c| } \hline & Miles& Time \\ \hline Diane & 3& 39 min. \\ Jane & 4&52 min.\\ Hector &5&65 min.\\ \hline \end{tabular}$

$\textup{Diane's Pace: }P_D=\frac{39\textup{ min.}}{3\textup{ miles}}=\frac{13\textup{min}}{1\textup{mile}}$

$\textup{Jane's Pace: }P_J=\frac{52\textup{ min.}}{4\textup{ miles}}=\frac{13\textup{min}}{1\textup{mile}}$

$\textup{Hector's Pace: }P_H=\frac{65\textup{ min.}}{5\textup{ miles}}=\frac{13\textup{min}}{1\textup{mile}}$

Step 3: Compare the paces to arrive at a solution.

Since,

$\\13=13=13 \\P_D=P_J=P_H$

therefore everyone's pace is the same.

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Example Question #12 : Average Rate Of Change: Ccss.Math.Content.Hsf If.B.6

Diane, Jane, and Hector participated in a relay race. The following table shows the distance they each ran and the amount of time it took them.

$\begin{tabular}{ |c|c|c|c| } \hline & Miles& Time \\ \hline Diane & 3& 38 min. \\ Jane & 4&35 min.\\ Hector &5&72 min.\\ \hline \end{tabular}$

Who had the fastest pace?

Possible Answers:

$\text{Hector}$

$\text{Jane and Diane}$

$\text{Jane}$

$\text{Diane}$

$\text{Diane and Hector}$

Correct answer:

$\text{Jane}$

Explanation:

This question is testing one's ability interpret a table and identify the rate of change.

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 average rate of change formula for calculations.

$\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

In the particular case, to find the fastest pace person, there will need to an average rate of change calculation done for each person to find their mile pace.

Step 2: Calculate the mile pace for Diane, Jane, and Hector.

$\textup{Diane's Pace: }P_D=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

$\textup{Jane's Pace: }P_J=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

$\textup{Hector's Pace: }P_H=\frac{\Delta \textup{Time}}{\Delta \textup{Miles}}$

Using the information provided by the table, calculate the pace of each individual.

$\begin{tabular}{ |c|c|c|c| } \hline & Miles& Time \\ \hline Diane & 3& 38 min. \\ Jane & 4&35 min.\\ Hector &5&72 min.\\ \hline \end{tabular}$

$\textup{Diane's Pace: }P_D=\frac{38\textup{ min.}}{3\textup{ miles}}=\frac{12.6\overline{6}\textup{min}}{1\textup{mile}}$

$\textup{Jane's Pace: }P_J=\frac{35\textup{ min.}}{4\textup{ miles}}=\frac{8.75\textup{min}}{1\textup{mile}}$

$\textup{Hector's Pace: }P_H=\frac{72\textup{ min.}}{5\textup{ miles}}=\frac{14.4\textup{min}}{1\textup{mile}}$

Step 3: Compare the paces to arrive at a solution.

Since,

$\\8.75<12.6\overline{6}<14.4 \\P_J<P_D<P_H$

therefore Jane is the fastest on the relay.

Report an Error

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:

$\textup{y-intercept}=1.5$

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

$\textup{y-intercept}=1$

$\textup{y-intercept}=2$

$\textup{y-intercept}=3$

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 #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:

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

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

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

$\textup{y-intercept}=1$

$\textup{y-intercept}=0$

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 #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:

$\textup{y-intercept}=2$

$\textup{y-intercept}=1$

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

$\textup{y-intercept}=5$

$\textup{y-intercept}=3$

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:

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

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

$\textup{y-intercept}=2$

$\textup{y-intercept}=1$

$\textup{y-intercept}=3$

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 #5 : 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:

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

$\textup{y-intercept}=4$

$\textup{y-intercept}=2$

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

$\textup{y-intercept}=3$

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:

$\textup{y-intercept}=3$

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

$\textup{y-intercept}=2$

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

$\textup{y-intercept}=0$

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:

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

$\textup{y-intercept}=1$

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

$\textup{y-intercept}=2$

$\textup{y-intercept}=3$

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 #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:

$\textup{y-intercept}=3$

$\textup{y-intercept}=1$

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

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

$\textup{y-intercept}=0$

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

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Common Core: High School - Functions : Interpreting Functions

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

All Common Core: High School - Functions Resources

Example Questions

Example Question #11 : Average Rate Of Change: Ccss.Math.Content.Hsf If.B.6

Example Question #12 : Average Rate Of Change: Ccss.Math.Content.Hsf If.B.6

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 #3 : 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 #5 : 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 #8 : Graph Linear And Quadratic Functions: Ccss.Math.Content.Hsf If.C.7a

All Common Core: High School - Functions Resources

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