The function is .

Domain :

The function .

The function continuous for all the points except at .

Thus, the domain of the function is .

Intercepts :

- intercept:

To find the - intercept, substitute in the function.

Thus, the function does not have  - intercept.

- intercept :

To find the - intercept, substitute in the function.

and

Thus, the function has - intercept at and .

Symmetry :

If , then the function is even function and it is symmetric about -axis.

If , then the function is odd function and it is symmetric about origin.

Here .

The function is even function.

Thus, the function is symmetric about -axis.

Asymptotes :

Vertical asymptote:

To find vertical asymptote of the function , equate denominator of the function 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.

Test intervals are and

\ Interval \	Test Value	Sign of	Conclusion
		\ \	Decreasing
		\ \	Increasing

Determination of extrema :

The function has a local minimum as the is changing its sign from negative to positive at .

As the function is not defined , the function has no 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
		\ \	\ Down \

Thus, the graph is concave down on the interval .

The graph is concave down on the interval .

Graph of the function using above specifications :

Graph of the function  is