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The function is $\"\"$ .

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Average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(a).

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The average rate of change from $\"\"$ to $\"\"$ .

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In this case $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$ .

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in $\"\"$ .

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Average rate of change $\"\"$ .

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$\"\"$

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The average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(b).

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The average rate of change from $\"\"$ to $\"\"$ .

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In this case $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in $\"\"$ .

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Average rate of change $\"\"$

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$\"\"$

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The average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(c).

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The average rate of change from $\"\"$ to $\"\"$ .

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In this case $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in $\"\"$ .

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Average rate of change $\"\"$

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$\"\"$

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The average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(d).

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The average rate of change from $\"\"$ to $\"\"$ .

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In this case $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in $\"\"$ .

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Average rate of change $\"\"$

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$\"\"$

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The average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(e).

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The average rate of change from $\"\"$ to $\"\"$ .

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In this case $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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Substitute $\"\"$ and $\"\"$ , $\"\"$ in $\"\"$ .

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Average rate of change $\"\"$

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$\"\"$

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The average rate of change from $\"\"$ to $\"\"$ is $\"\"$ .

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(f).

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A secant line is a straight line joining two points of a function.

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The function $\"\"$ is passes through origin.

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The line equation passes through origin is $\"\"$ .

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Average rate of change is the slope of the secant line.

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The secant lines are $\"\"$ , $\"\"$ , $\"\"$ , $\"\"$ , and $\"\"$ .

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Graph :

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Graph of the function and secant lines:

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$\"\"$

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(g).

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Observe graph:

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The secant lines are getting closer to the tangent line at $\"\"$ .

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(h).

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The slopes of the secant lines are decreasing. They are getting closer to $\"\"$ .

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(a). $\"\"$

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(b). $\"\"$

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(c). $\"\"$

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(d). $\"\"$

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(e). $\"\"$

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(f). Graph of the function and secant lines is

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$\"\"$

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(g). They are getting closer to the tangent line at $\"\"$ .

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(h). The slopes of the secant lines are decreasing.They are getting closer to $\"\"$ .