The function is .

The domain of a function is all possible values of .

The domain of the function is .

Intercept :

To find the -intercept, substitute  in the function.

Apply zero product property.

 and 

 and 

 and .

The -intercepts are  and .

To find the -intercept, substitute  in the function.

The -intercept is .

Find the extrema.

The function is .

Apply derivative on each side  with respect to .

Apply product rule of derivatives: .

In this case  and .

.

To find the critical numbers by equating .

.

The critical numbers are .

.

The domain of is .

Relative extrema points exist at critical numbers.

The test intervals are ,  and .

Perform first derivative test to identify the nature of the extrema.

Test itervals	Test value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing
		\ \	Increasing
		\ \	Decreasing

The function has relative maximum at .

Substitute  in .

The relative minimum at .

Substitute  in .

The relative maximum at .

Inflection points:

.

Again apply derivative on each side with respect to .

Apply quotient rule of derivatives: .

Find inflection points by equating .

 and 

 and 

 and 

 and .

 is not in the domain.

Therefore, there is inflection point is at .

Substitute  in .

The inflection point is .

Consider the test intervals as .

\ Interval \	Test Value	Sign of	Concavity
		\ \	\ Up \
		\ \	Down

Asymptotes :

Vertical asymptote:

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

The function is .

There is no vertical asymptote.

Horizontal asymptote:

The line  is called a horizontal asymptote of the curve  if either \ \   or 

.

.

There is no horizontal asymptote.

Graph:

Graph the function .

Graph:

Graph the function .

.