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

 and .

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 at , the functionis not defined .

Therefore the -intercepts is .

(C)

Symmetry :

Substitute  in the function.

Here 

Therefore the function  is neither odd nor even.

(D)

Asymptotes :

Horizontal asymptote :

Therefore the horizontal asymptote is .

Vertical asymptote :

Vertical asymptote appears when the function is not defined.

Since at , the functionis not defined. 

Therefore the vertical asymptote is .

(E)

Intervals of increase or decrease : 

The function is .

Differentiate  on each side with respect to .

 is never zero and the function is positive for the domain of .

Therefore  is increasing over its domain.

(F)

Local Maximum and Minimum values :

From (E) it is clear that the function is only increasing.

Therefore is no local minimum or maximum values.

(G)

Concavity and point of inflection :

.

Differentiate  on each side with respect to .

Find inflection point.

 is never zero.

There is no inflection point.

But at  and , the function is undefined, so split the intervals into ,   and .

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

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) No symmetry.

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

(E) Increasing on  , and .

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

(G) Concave up on  and .

      concave down on .

(H) Graph of the function   is

.