The function is .

(A)

Domain :

The function is .

All possible values of is the domain of the function.

Denominator of the function should not be zero

The domain of the function is .

(B)

Intercepts :

To find the -intercepts, substitute in the function.

.

Therefore the -intercept is .

To find the -intercepts, substitute in the function.

Since never be zero.

Therefore there is no  -intercepts.

(C)

Symmetry :

Substitute in the function.

.

Therefore the function is an even.

(D)

Asymptotes :

Horizontal asymptote :

Therefore the horizontal asymptote is .

Vertical asymptote :

Vertical asymptote appears when the function is not defined.

Therefore the vertical asymptote are and .

(E)

Intervals of increase or decrease : 

The function is .

Differentiate on each side with respect to .

.

Find critical points by equating .

Test intervals are based on and where is undefined.

Test intervals are , , and .

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

The graph is increasing in the interval , .

The graph is decreasing in the interval , .

(F)

Local Maximum and Minimum values :

The function has a local maximum at , because changes its sign from positive to negative.

Substitute in .

.

Local maximum is .

(G)

Concavity and point of inflection :

.

Differentiate on each side with respect to .

Since never be zero, there is no inflection points.

But at and , the function is undefined,hence consider those points also.

Split the intervals into , and .

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

The graph is concave up in the interval , .

The graph is concave down in the interval .

(H)

Graph :

Graph of the function  :

(A) The domain of the function is .

(B) -intercept is and -intercepts are .

(C) Even symmetry about -axis.

(D) The horizontal asymptote is and the vertical asymptotes are and .

(E) The graph is increasing in the interval , .

The graph is decreasing in the interval , .

(F) There is neither local minimum nor local maximum.

(G) Concave up on , .

      concave down on .

(H) Graph of the function  is