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.

Here denominator of the function $\"\"$ .

Therefore, 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.

$\"\"$

Hence $\"\"$ .

Therefore the function $\"\"$ is an even function.

The function is symmetric about $\"\"$ -axis.

(D)

Asymptotes :

Horizontal asymptote :

$\"\"$

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

Vertical asymptote :

Vertical asymptote appears when the function is not defined.

The function is defined for all real numbers.

Therefore, there are no vertical asymptotes.

(E)

Intervals of increase or decrease :

The function is $\"\"$ .

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

$\"\"$

$\"\"$ .

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

$\"\"$

$\"\"$ .

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

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

Interval

Test Value

Sign of

\"\"

Conclusion

\"\"

\"\"

$\"\"$

Decreasing

\"\"

\"\"

$\"\"$

Increasing

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 minimum at $\"\"$ , because $\"\"$ changes its sign from negative to positive.

Substitute $\"\"$ in $\"\"$ .

$\"\"$ .

Local minmum is $\"\"$ .

(G)

Concavity and point of inflection :

$\"\"$ .

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

$\"\"$

$\"\"$ .

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

$\"\"$

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

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

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

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

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

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

(H)

Graph :

Graph of the function $\"\"$ :

$\"\"$

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

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

(D) The horizontal asymptote is $\"\"$ and there is no vertical asymptotes.

(E) The graph is increasing in the interval $\"\"$ .

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

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

(G)

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

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

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

$\"\"$