The function is .

Domain :

The function

The function is continuous for all the points except at .

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 neither even nor odd.

Asymptotes :

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

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 :

Differentiate with respect to :

is never zero on its domain.

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.

Hence, there is no inflection points.

But at the function is undefined.

Consider the test intervals as and

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

Thus, the graph is concave up on the interval .

The graph is concave down on the interval .

Graph of the function  :  

Graph of the function  :  

.