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  :

.