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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 #161 : High School: Functions

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&10 \\ 1&4 \\ 2&3 \\ 2.5 & 1 \\ 3&3\\ 4&4 \\ 5&10\\ \hline \hline \end{tabular}$ Q11

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

Possible Answers:

$\text{No minimum exists}$

$\text{More information is needed}$

$\text{Table}$

$\text{Graph and table are equal}$

$\text{Graph}$

Correct answer:

$\text{Graph}$

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 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) .

Q11

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.

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Example Question #162 : High School: Functions

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&5 \\ 2&5.5 \\ 2.5 & 5.75 \\ 3&5.5\\ 4&5 \\ 5&0\\ \hline \hline \end{tabular}$

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

Possible Answers:

$\text{Table}$

$\text{More information is needed}$

$\text{No maximum exists}$

$\text{Graph}$

$\text{Table and graph are equal}$

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.

$\begin{tabular}{||c c||} \hline Time & Distance \\ [0.5ex] \hline\hline 0&0 \\ 1&5 \\ 2&5.5 \\ {\color{Red} 2.5} & {\color{Red} 5.75} \\ 3&5.5\\ 4&5 \\ 5&0\\ \hline \hline \end{tabular}$

Recall that the time represents the values while the distance represents the values. Therefore the ordered pair for the maximum can be written as (2.5,5.75) .

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.

$4.25<5.75\Rightarrow \textup{Graph}< \textup{Table}$

Therefore, the table has the largest maximum.

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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 #161 : High School: Functions

Example Question #162 : High School: Functions

All Common Core: High School - Functions Resources

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