The function is .

Domain :

The function .

The function is continuous for all the points except at and .

Thus the domain of the function is .

Intercepts :

Find the -intercept by substituting :

Thus, -intercept is .

Find the -intercept by substituting .

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.

Here .

Thus, the function is odd and it is symmetric about origin.

Asymptotes :

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

Vertical asymptotes are at 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 with respect to :

is never zero on its domain.

is undefined  when and .

is increasing on its domain because

Determination of extrema :

is an increasing function, hence there is no chance of local minimum or maximum.

Determination of inflection point:

Differentiate with respect to :

.

is never zero on its domain.

is undefined  when and .

Equate to zero.

Real solution is .

Inflection point is .

Consider the test intervals as , , and .

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

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

The graph is concave down on the interval and .

Graph of the function  :  

Graph of the function :  

.