The function is and interval is .

Find the intercepts :

To find the - intercept, substitute in the function.

Solve in the interval .

and

and .

doesnot exist for real values of .

The solutions of are , and in the interval .

Therefore, the - intercepts are , and .

To find the -intercept, substitute in the function.

The - intercept is .

Find the relative extrema for the function :

Consider .

Differentiate on each side with respect to .

To find the critical number, make .

and

and

The solutions of are and in the interval .

There is no solution for in the interval .

Thus, the critical points occur at and .

If , then .

If , then .

The relative maximum is .

The relative minimum is .

Find the points of inflection :

 Consider .

Derivative on each side with respect to .

To find inflection points, equate to zero.

and

and

, , and .

The solutions of are , and in the interval .

The solutions of are and in the interval .

The solutions of are and in the interval .

If , then .

If , then .

If , then .

If , then .

If , then .

If , then .

If , then .

The inflection points are , , , , , , and .

Find the asymptotes :

The function is .

Vertical asymptote :

The line is a vertical asymptote if .

Therefore, there is no vertical asymptote for the function .

Horizontal asymptote :

The line is a horizontal asymptote if .

Limit does not exist.

Therefore, there is no horizontal asymptote for the function .

Find intervals of increase or decrease :

Consider the test intervals as ,   and .

\ Interval \	Test Value	Sign of	Sign of	Conclusion
			\ \	Increases, point of inflection
			\ \	Decreases, concave downward
			\ \	Increases,point of inflection

The graph is increases on the intervals and .

The graph is decreases on the interval .

Using all the above characteristics of the function, graph the function in the interval .

Graph :

Draw a coordinate plane.

Graph the function in the interval .

.

The function is in the interval .

Graph :

Using Graphing utility draw the graph of the function in the interval ..

.

Observe the above two graphs : The graphs represents the same function, i.e, .

Graph of the function in the interval :

.