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All Common Core: High School - Functions Resources

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Flashcards: 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?

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

$\textup{More information is needed.}$

$\text{No maximum exists. }$

$\textup{Figure 1}$

$\textup{Table 1}$

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Flashcards: Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

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

Your answer:

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

Your answer:

$\textup{More information is needed.}$

Your answer:

$\text{No maximum exists. }$

Your answer:

$\textup{Table 1}$

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.

Flashcards: 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?

$\text{More information is needed.}$

$\text{No maximum exists. }$

$\text{Table}$

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

$\text{Graph}$

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Flashcards: 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?

Your answer:

$\text{More information is needed.}$

Your answer:

$\text{No maximum exists. }$

Your answer:

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

Your answer:

$\text{Graph}$

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 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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All Common Core: High School - Functions Resources

Flashcards: Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

Flashcards: Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

Flashcards: Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

Flashcards: Compare Function Properties: CCSS.Math.Content.HSF-IF.C.9

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