The function is .

Domain:

The function .

The function  continuous for all the points except at .

Thus, the domain of the function is .

Intercepts:

Find the -intercept by substituting :

Thus, the function does not have   - intercept.

Find the -intercept by substituting .

 and .

Thus, -intercepts are  and .

Symmetry :

If , then the function  is even function and it is symmetric about -axis.

If , then the function  is odd function and it is symmetric about origin.

Here .

The function  is even function.

Thus, the function  is symmetric about -axis.

Asymptotes:

Vertical asymptote:

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

The function .

The vertical asymptote is .

Horizontal asymptote:

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

  or 

Thus, the horizontal asymptote is .

Intervals of increase or decrease:

Apply derivative on each side with respect to .

.

 is never zero on its domain.

 is undefined  when .

\ Interval \	Test Value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing

Determination of extrema :

The function has a local minimum as the  is changing its sign from negative to positive at .

As the function is not defined , the function  has no local minimum or maximum.

Determination of inflection point:

Apply derivative on each side with respect to .

.

 is never zero.

Hence, there is no inflection points.

At  the function is undefined.

Consider the test intervals as  and .

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

Thus, the graph is concave down on the interval .

The graph is concave down on the interval .

Graph of the function  :

Graph of the function  :

.