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.

$\"\"$

Therefore the $\"\"$ -intercept is $\"\"$ .

(C)

Symmetry :

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

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.

The function is not defined at $\"\"$ .

Therefore the vertical asymptote is $\"\"$ .

(E)

Intervals of increase or decrease :

The function is $\"\"$ .

Differentiate on each side with respect to $\"\"$ .

$\"\"$

$\"\"$ .

Find critical points by equating $\"\"$ .

$\"\"$

$\"\"$ .

The function is undefined at $\"\"$ .

Critical points are $\"\"$ and $\"\"$ .

Test intervals are $\"\"$ , $\"\"$ and $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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

The graph is increasing in the interval $\"\"$ .

The graph is decreasing in the interval $\"\"$ and $\"\"$ .

(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 $\"\"$ .

$\"\"$

$\"\"$ .

Find inflection points by equating $\"\"$ to zero.

$\"\"$

$\"\"$ and $\"\"$ .

At $\"\"$ , $\"\"$ .

Inflection points are $\"\"$ and $\"\"$ .

Test intervals are $\"\"$ , $\"\"$ , $\"\"$ and $\"\"$ .

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \

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

The graph is concave up in the interval $\"\"$ and $\"\"$ .

The graph is concave down in the interval $\"\"$ and $\"\"$ .

(H)

Graph :

Graph of the function $\"\"$ :

$\"\"$

(A) The domain of the function $\"\"$ is $\"\"$ .

(B) $\"\"$ -intercept $\"\"$ and $\"\"$ -intercept is $\"\"$ .

(D) The horizontal asymptote is $\"\"$ and the vertical asymptote is $\"\"$ .

(E)

The graph is increasing in the interval $\"\"$ .

The graph is decreasing in the interval $\"\"$ and $\"\"$ .

(F) Local maximum is $\"\"$ .

(G)

The graph is concave up in the interval $\"\"$ and $\"\"$ .

The graph is concave down in the interval $\"\"$ and $\"\"$ .

Inflection points are $\"\"$ and $\"\"$ .

(H) Graph of the function $\"\"$ is

$\"\"$ .