$\"\"$

The function is $\"\"$ .

Domain :

The function is $\"\"$ .

The function $\"\"$ continuous for all the points.

Thus, the domain of the function $\"\"$ is all real numbers.

Intercepts :

$\"\"$ - intercept is $\"\"$ :

$\"\"$

Thus, $\"\"$ - intercept is $\"\"$ .

$\"\"$ - intercept :

Consider $\"\"$ and solve for $\"\"$ .

$\"\"$

Thus, $\"\"$ - intercept is $\"\"$ .

$\"\"$

Symmetry :

If $\"\"$ , then the function $\"\"$ is even and it is symmetric about $\"\"$ -axis.

If $\"\"$ , then the function $\"\"$ is odd and it is symmetric about origin.

$\"\"$

Since $\"\"$ , the function $\"\"$ is an even function.

Since the function $\"\"$ ia an even function, the graph of the function is symmetric about $\"\"$ -axis.

$\"\"$

Asymptotes :

Vertical asymptote :

Vertical asymptote exist when denominator is zero.

Equate denominator to zero.

$\"\"$

There is no real values for $\"\"$ .

So there is no vertical asymptotes.

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 :

$\"\"$ .

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

$\"\"$

$\"\"$ .

$\"\"$

Determination of inflection point :

$\"\"$ .

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

$\"\"$

$\"\"$ .

Equate $\"\"$ to zero.

$\"\"$

If $\"\"$ , $\"\"$ .

Thus, the inflection points are $\"\"$ and $\"\"$ .

Consider the test intervals as $\"\"$ , $\"\"$ and $\"\"$ .

\ \

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

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

Thus, the graph is concave up on the intervals $\"\"$ and $\"\"$ .

The graph is concave down on the interval $\"\"$ .

$\"\"$

Graph of the function $\"\"$ :

$\"\"$

Graph of the function $\"\"$ :

$\"\"$ .