\

The function is $\"\"$ .

\

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

\

(a).

\

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

\

In this case $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ .

\

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

\

$\"\"$

\

$\"\"$ .

\

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

\

Average rate of change $\"\"$

\

$\"\"$

\

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

\

\

(b).

\

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

\

In this case $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

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

\

Average rate of change $\"\"$

\

$\"\"$

\

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

\

\

(c).

\

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

\

In this case $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

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

\

Average rate of change $\"\"$

\

$\"\"$

\

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

\

\

(d).

\

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

\

In this case $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

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

\

Average rate of change $\"\"$

\

$\"\"$

\

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

\

\

(e).

\

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

\

In this case $\"\"$ .

\

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

\

$\"\"$

\

$\"\"$

\

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

\

Average rate of change $\"\"$

\

$\"\"$

\

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

\

\

(f).

\

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

\

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

\

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

\

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

\

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

\

Graph :

\

Graph of the function and secant lines :

\

$\"\"$

\

\

(g).

\

Observe graph:

\

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

\

\

(h).

\

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

\

\

(a). $\"\"$

\

(b). $\"\"$

\

(c). $\"\"$

\

(d). $\"\"$

\

(e). $\"\"$

\

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

\

$\"\"$

\

(g). The secant lines are getting closer to the line $\"\"$ .

\

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