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a.

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The parent function is $\"\"$ .

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Graph :

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Graph of the function $\"\"$ for $\"\"$ .

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$\"\"$

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b.

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Find the average rate of change of each function on the interval $\"\"$ at $\"\"$ .

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Average rate of change on the interval $\"\"$ is $\"\"$ .

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Substitute corresponding values in above formula.

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Average rate of change :

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$\"\"$

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ .

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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c.

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The value of b increases average rate of change for the function $\"\"$ also increases.

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Graph of the function is expanded vertically which is shown graphs in part a.

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d.

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Graph of the function $\"\"$ for $\"\"$ .

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$\"\"$

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e.

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Find the average rate of change of each function on the interval $\"\"$ .

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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Average rate of change for the function on the interval $\"\"$ at $\"\"$ .

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$\"\"$

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$\"\"$ .

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f. \ \

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The value of b increases, average rate of change for the function $\"\"$ also decreases.

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Graphs that have larger values for b are greater for negative values of x, but when x is positive, the graphs decrease and

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approach 0 faster.

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$\"\"$

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a.

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Graph of the function $\"\"$ for $\"\"$ .

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$\"\"$

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b.

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is 1.5.

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is 4.

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is 7.5.

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is 12.

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c.

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The value of b increases average rate of change for the function $\"\"$ also increases.

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Graph of the function is expanded vertically which is shown graphs in part a.

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d.

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Graph of the function $\"\"$ for $\"\"$ .

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$\"\"$

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e.

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is $\"\"$ .

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is $\"\"$ .

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is $\"\"$ .

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Average rate of change of each function on the interval $\"\"$ at $\"\"$ is $\"\"$ .

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f.

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The value of b increases, average rate of change for the function $\"\"$ also decreases.

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Graphs that have larger values for b are greater for negative values of x, but when x is positive, the graphs decrease and

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approach 0 faster.