The function is .

Domain:

The function .

The function continuous for all the points except at .

Thus, the domain of the function is .

Intercepts :

Find the -intercept by substituting :

Thus, the function does not have  - intercept.

Find the -intercept by substituting .

.

Thus, -intercept is .

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 and .

Therefore, the function is neithe even nor odd.

Asymptotes :

Vertical asymptote :

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

The function .

.

The 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:

.

Apply derivative on each side with respect to .

.

.

is never zero on its domain.

is undefined when .

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

Determination of extrema :

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

Determination of inflection point:

.

Apply derivative on each side with respect to .

.

is never zero.

Hence, there is no inflection points.

At the function is undefined.

Consider the test intervals as and .

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

Thus, the graph is concave down on the interval .

The graph is concave up on the interval .

Graph of the function :

Graph of the function :

.