The function is .

Domain :

Thu function .

The function continuous for all the points.

Thus, the domain of the function is all real numbers.

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 and it is about - axis.

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.

There is no real values for .

So there is no vertical asymptotes.

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 .

.

Determination of inflection point :

.

Differentiate on each side with respect to .

.

Equate to zero.

If , .

If , .

Thus, the inflection points are and .

Consider the test intervals as , and

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

Thus, the graph is concave up on the intervals and .

The graph is concave down on the interval .

Graph of the function :

.

Graph of the function :

.