The function is .

Domain :

The function .

The denominator of the function should not be zero.

The function continuous for all the points except at .

Thus, the domain of the function is .

Intercepts :

- intercept is :

Thus, - intercept is .

 - intercept :

Consider and solve for x.

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 :

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 on each side  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 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 \

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  :

.