The function is .

Intercepts :

Find the - intercept by substituting  in .

The -intercepts are  and .

Find the -intercept by substituting  in .

The -intercept is .

Find the relative extrema for the function  :

Consider .

Differentiate on each side with respect to .

Find the critical numbers by solving .

The solution of   are  and  in the interval .

Thus, the critical points occur at  and .

If , then .

If , then .

The relative maximum is .

The relative minimum is .

Find the inflection points :

Consider .

Equate  to .

The solutions of  are ,  and  in the interval .

If , then .

If , then .

If , then .

The inflection points are , , and .

Find the asymptotes :

The function is .

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
		\ \	\ \	Decreases, concave upward
			\ \	\ Increases, point of inflection \
			\ \	Decreases, point of inflection

The graph is increases on the intervals  .

The graph is decreases on the interval  and .

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  :

.