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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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All Common Core: High School - Functions Resources

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Example Questions

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Example Question #7 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Determine the percent rate of change and whether the function represents exponential growth or decay.

y=(0.34)^x

Possible Answers:

$\\ \textup{Percent rate of change: } 34\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 66\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 67\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 34\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 66\% \\ \textup{Exponential Growth}$

Correct answer:

$\\ \textup{Percent rate of change: } 66\% \\ \textup{Exponential Decay}$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent rate of change.

For the purpose of Common Core Standards, properties of exponents to interpret functions falls within the Cluster C of analyze functions using different representations concept (CCSS.MATH.CONTENT.HSF-IF.C.8).

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 what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Calculate the percent rate of change.

Recall that in the previous expressions represent the rate. Therefore, to calculate the percent rate of change simply multiply by 100.

Step 4: Answer question.

Following the above steps to solve this particular question, results in the following.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2:

Use algebraic techniques to aid in solving the problem.

Given the function,

y=(0.34)^x

use the above expressions to help solve.

Since

0.34=1-r; r=0.66

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.34=1-r; r=0.66

therefore to solve for percent rate of change multiply by 100.

$0.66\times 100=66\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 66\% \\ \textup{Exponential Decay}$

Report an Error

Example Question #8 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Determine the percent rate of change and whether the function represents exponential growth or decay.

y=(0.89)^x

Possible Answers:

$\\ \textup{Percent rate of change: } 11\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 11\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 89\% \\ \textup{Exponential Growth}$

$\\ \textup{Percent rate of change: } 10\% \\ \textup{Exponential Decay}$

$\\ \textup{Percent rate of change: } 89\% \\ \textup{Exponential Decay}$

Correct answer:

$\\ \textup{Percent rate of change: } 11\% \\ \textup{Exponential Decay}$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent 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 what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Calculate the percent rate of change.

Recall that in the previous expressions represent the rate. Therefore, to calculate the percent rate of change simply multiply by 100.

Step 4: Answer question.

Following the above steps to solve this particular question, results in the following.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2:

Use algebraic techniques to aid in solving the problem.

Given the function,

y=(0.89)^x

use the above expressions to help solve.

Since

0.89=1-r; r=0.11

the functions can be defined as exponential growth.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.89=1-r; r=0.11

therefore to solve for percent rate of change multiply by 100.

$0.11\times 100=11\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 11\% \\ \textup{Exponential Decay}$

Report an Error

Example Question #9 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

A savings account has an interest rate of $1.5\%$ compounded annually. If Bob deposits $\$55.00$ into the account how much money will he have in his savings account after years?

Possible Answers:

$\$60.14$

$\$59.10$

$\$65.14$

$\$62.27$

$\$66.70$

Correct answer:

$\$60.14$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent rate of change and function values at specific input values.

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 what the question is asking for.

The question is asking for the Bob's account balance after 6 years.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Identify what is known.

$\\r=\textup{rate}=1.5\% \\a=\textup{Initial Deposit}=\$55.00 \\x=\textup{Time}=6$

Step 4: Substitute the known values into the growth function.

$\\f(6)=a(1+r)^x \\f(6)=\$55.00(1+.015)^6 \\f(6)=\$55.00(1.0934) \\f(6)=\$60.14$

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Example Question #10 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Janet has a student loan of $\$3\textup,500$ . The company that is financing the loan has an annual interest rate of $2.67\%$ . If Janet waits two years to start paying off her loan, how much interest will have accumulated?

Possible Answers:

$\$189.14$

$\$198.40$

$\$190.40$

$\$189.40$

$\$2.40$

Correct answer:

$\$189.40$

Explanation:

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 what the question is asking for.

The question is asking for the amount of interest that will be added to the loan after two years.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Identify what is known.

$\\r=\textup{rate}=2.67\% \\a=\textup{Initial Deposit}=\$3500.00 \\x=\textup{Time}=2$

Step 4: Substitute the known values into the growth function.

$\\f(2)=a(1+r)^x \\f(6)=\$3500.00(1+.0267)^2 \\f(2)=\$3689.40$

Step 5: Calculate the amount of interest.

To calculate the amount of interest, subtract the initial amount from the final amount found in step 4.

$\\ \textup{Interest}=\textup{Final Amount}-\textup{Initial Amount} \\\textup{Interest}=\$3689.40-\$3500.00 \\\textup{Interest}=\$189.40$

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Example Question #11 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Given the following function determine if it is exponentially growing or decaying and the function value when is .

f(x)=1.2(0.72)^x

Possible Answers:

$\\ f(3)=1.448 \\ \textup{Exponential Decay}$

$\\ f(3)=0.448 \\ \textup{Exponential Decay}$

$\\ f(3)=0.448 \\ \textup{Exponential Growth}$

$\\ f(3)=0.648 \\ \textup{Exponential Decay}$

$\\ f(3)=1.448 \\ \textup{Exponential Growth}$

Correct answer:

$\\ f(3)=0.448 \\ \textup{Exponential Decay}$

Explanation:

This question is testing one's ability to use properties of exponents to solve and interpret functions as well as identify key concepts of exponential growth and decay such as percent 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 what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the function value at 3.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Calculate the percent rate of change.

Recall that in the previous expressions represent the rate. Therefore, to calculate the percent rate of change simply multiply by 100.

Step 4: Answer question.

Following the above steps to solve this particular question, results in the following.

Step 1: Identify what the question is asking for.

Find whether the given function is exponential growth or decay after which, find the percent rate of change.

Step 2:

Use algebraic techniques to aid in solving the problem.

Given the function,

f(x)=1.2(0.72)^x

use the above expressions to help solve.

Since

0.72=1-r; r=0.28

the functions can be defined as exponential decay.

Step 3: Calculate the percent rate of change.

From the previous step it was found that,

0.72=1-r; r=0.28

therefore to solve for percent rate of change multiply by 100.

$0.28\times 100=28\%$ .

Step 4: Answer question.

$\\ \textup{Percent rate of change: } 28\% \\ \textup{Exponential Decay}$

Step 5: Find the function value at 3.

$\\f(x)=1.2(0.72)^x \\f(3)=1.2(0.72)^3 \\f(3)=0.4479\\f(3)=0.448$

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Example Question #12 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Tina invests $\$1\textup,250$ into an account where it accumulates at an interest rate of $3.7\%$ annually. After years how much money does Tina have?

Possible Answers:

$\$1997.62$

$\$1787.62$

$\$1897.62$

$\$1797.62$

$\$1977.62$

Correct answer:

$\$1797.62$

Explanation:

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 what the question is asking for.

The question is asking for the amount of money Tina has many after investing for ten years.

Step 2: Use algebraic techniques to aid in solving the problem.

I. a(1+r)^x represents an exponential growth function.

II. a(1-r)^x represents an exponential decay function.

Step 3: Identify what is known.

$\\r=\textup{rate}=3.7\% \\a=\textup{Initial Deposit}=\$1250.00 \\x=\textup{Time}=10$

Step 4: Substitute the known values into the growth function.

$\\f(10)=a(1+r)^x \\f(10)=\$1250.00(1+.037)^{10} \\f(10)=\$1797.62$

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Example Question #1 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\textup{ Table 1} \\\\ \begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$ Screen shot 2016 01 13 at 7.10.56 pm

The above table and figure describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{No maximum exists. }$

$\textup{Table 1}$

$\textup{Figure 1}$

$\textup{Figure 1 and Table 1 are equal.}$

$\textup{More information is needed.}$

Correct answer:

$\textup{Figure 1}$

Explanation:

This question is testing one's ability to compare the properties of functions when they are illustrated in different forms. This question specifically is asking for the examination and interpretation of two quadratic functions for which one is illustrated in a table format and the other is illustrated graphically.

For the purpose of Common Core Standards, "Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions)." falls within the Cluster C of "Analyze Functions Using Different Representations" concept (CCSS.MATH.CONTENT.HSF-IF.C.9).

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\textup{ Table 1} \\\\ \begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Now, let us plot the points from the table and connect them with a smooth curve to represent the function.

Screen shot 2016 01 13 at 7.03.33 pm

It is seen from the table and the graph that the vertex or maximum of the function exists at (2.5,6.25) .

Step 2: Identify the maximum of Figure 2.

Screen shot 2016 01 13 at 7.10.56 pm

Looking at Figure 1, plotting the vertex and extending a vertical and horizontal line, we can find the coordinate pair of the vertex.

Therefore the vertex or maximum of Figure 1 is (2.5,9.25) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$6.25<9.25\Rightarrow \textup{Table 1}< \textup{Figure 1}$

Therefore, Figure 1 has the largest maximum.

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Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{Graph}$

$\text{The table and graph have the same maximum.}$

$\text{No maximum exists. }$

$\text{More information is needed.}$

$\text{Table}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a parabola opening down, occurs at the peak where the vertex lies.

For this particular graph the vertex is at (2,3) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$3<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

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Example Question #3 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a larger maximum?

Possible Answers:

$\text{Graph}$

$\text{Graph and Table}$

$\text{No maximum exists. }$

$\text{Table}$

$\textup{More information is needed.}$

Correct answer:

$\text{Table}$

Explanation:

Step 1: Identify the maximum of Table 1.

Using the table find the time value where the largest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,6.25) .

Step 2: Identify the maximum of the graph

Recall that the maximum of a cubic function is known as a local maximum. This occurs at the vertex of the peak on the graph which in this particular case, is at the point (-1,1) .

Step 3: Compare the maximums from step 1 and step 2.

Compare the value coordinate from both maximums.

$1<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #4 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ 2.5 & 1 \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

The table and graph describe two different particle's travel over time. Which particle has a lower minimum?

Possible Answers:

$\text{More information is needed}$

$\text{Table}$

$\text{Graph}$

$\text{Table and Graph are equal}$

$\text{No minimum exists}$

Correct answer:

$\text{Graph}$

Explanation:

Step 1: Identify the minimum of the table.

Using the table find the time value where the lowest distance exists.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ {\color{Red} 2.5} & {\color{Red} 1} \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the minimum can be written as (2.5,1) .

Step 2: Identify the minimum of the graph

Recall that the minimum of a cubic function is known as a local minimum. This occurs at the valley where the vertex lies.

For this particular graph the vertex is at (1,-3) .

Step 3: Compare the minimums from step 1 and step 2.

Compare the value coordinate from both minimums.

$-3<1\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

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 #7 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #8 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #9 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #10 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #11 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #12 : Properties Of Exponents: Ccss.Math.Content.Hsf If.C.8b

Example Question #1 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #2 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #3 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #4 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

All Common Core: High School - Functions Resources

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