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Common Core: High School - Functions : Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

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Example Questions

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:

$\textup{More information is needed.}$

$\text{No maximum exists. }$

$\textup{Figure 1}$

$\textup{Table 1}$

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

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.

Report an Error

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:

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

$\text{No maximum exists. }$

$\text{More information is needed.}$

$\text{Graph}$

$\text{Table}$

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.

Report an Error

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:

$\text{No maximum exists. }$

$\text{Graph and Table}$

$\text{Graph}$

$\textup{More information is needed.}$

$\text{Table}$

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 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 #2 : 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:

$\text{Table}$

$\text{No minimum exists}$

$\text{Table and Graph are equal}$

$\text{Graph}$

$\text{More information is needed}$

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

Example Question #5 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ 2.5 & 6.25 \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

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

Possible Answers:

$\text{Table}$

$\text{Graph}$

$\text{Graph and Table}$

$\text{More information is needed.}$

$\text{There is no minimum.}$

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.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ {\color{Red} 2.5} & {\color{Red}6.25} \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

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

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up, occurs at the valley where the vertex lies.

For this particular graph the vertex is at (4,3) .

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

Compare the value coordinate from both minimums.

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

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #6 : 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:

$\text{More information is needed}$

$\text{Table}$

$\text{No maximum exists}$

$\text{Table and Graph are equal}$

$\text{Graph}$

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 (-1.25,4.25) .

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

Compare the value coordinate from both maximums.

$4.25<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

Example Question #7 : 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:

$\text{Table and graph are equal}$

$\text{More information is needed.}$

$\text{No maximum exists.}$

$\text{Graph}$

$\text{Table}$

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 occurs at the vertex of the peak on the graph which in this particular case, is at the point (0,3)

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.

Report an Error

Example Question #8 : 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:

$\text{More information is needed.}$

$\text{Graph}$

$\text{Table}$

$\text{Table and graph are equal}$

$\text{No maximum exists.}$

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 occurs at the vertex of the peak on the graph which in this particular case, is at the point (4,5)

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

Compare the value coordinate from both maximums.

$5<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

Report an Error

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

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ 2.5 & 6.25 \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

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

Possible Answers:

$\text{More information is needed}$

$\text{Graph and table are equal}$

$\text{Graph}$

$\text{Table}$

$\text{No minimum is exists}$

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.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&12 \\ 1&9 \\ 2&7 \\ {\color{Red} 2.5} & {\color{Red} 6.25} \\ 3&7\\ 4&9 \\ 5&12\\ \hline \hline \end{tabular}$

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

Step 2: Identify the minimum of the graph

Recall that the minimum of a parabola opening up occurs at the valley where the vertex lies.

For this particular graph the vertex is at (4,5) .

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

Compare the value coordinate from both minimums.

$5<6.25\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the graph has the lowest minimum.

Report an Error

Example Question #10 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&4 \\ 2&6 \\ 2.5 & 6.25 \\ 3&6\\ 4&4 \\ 5&0\\ \hline \hline \end{tabular}$ Q10

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

Possible Answers:

$\text{Table}$

$\text{Graph}$

$\text{Table and graph are equal}$

$\text{No maximum exists}$

$\text{More information is needed}$

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) .

Q10

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

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Common Core: High School - Functions : Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

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

All Common Core: High School - Functions Resources

Example Questions

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

Example Question #5 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #6 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #7 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

Example Question #8 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

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

Example Question #10 : Compare Function Properties: Ccss.Math.Content.Hsf If.C.9

All Common Core: High School - Functions Resources

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