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

## Example Questions

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### Example Question #1 : 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?

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.

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

It is seen from the table and the graph that the vertex or maximum of the function exists at .

Step 2: Identify the maximum of Figure 2.

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 .

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

Compare the  value coordinate from both maximums.

Therefore, Figure 1 has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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 .

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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 .

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

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 .

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

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

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 .

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

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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 .

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the minimum can be written as .

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 .

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

Compare the  value coordinate from both minimums.

Therefore, the graph has the lowest minimum.

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

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

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.

Recall that the time represents the  values while the distance represents the  values. Therefore the ordered pair for the maximum can be written as .

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 .

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

Compare the  value coordinate from both maximums.

Therefore, the table has the largest maximum.

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