The function is .

Domain :

The function .

The function  continuous for all the points except at .

Because at  the function is undefined.

Thus, the domain of the function  is .

Intercepts :

 - intercept is :

Thus,  - intercept is .

 - intercept :

Consider  and solve for .

Thus,  - intercept is .

Symmetry :

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

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

Since , the function  is an even function.

Since the function  is an even function, the graph of the function is symmetric about  - axis.

Asymptotes :

Vertical asymptote :

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

Vertical asymptotes are  and .

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 :

Differentiate on each side with respect to .

.

Equate  to zero.

Thus, the function  has a local maximum at . 

Determination of inflection point :

Since  is an continuous function, there is a local maximum at .

.

Differentiate on each side with respect to .

.

 is never zero.

Hence, there is no inflection points.

But at  the function is undefined.

Consider the test intervals as  ,  and 

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

Thus, the graph is concave up on the intervals .

The graph is concave down on the intervals  and .

Graph of the function  :

Graph of the function  :

.