$\"\"$

The function is $\"\"$ .

The domain of the function is all real numbers except $\"\"$ .

Intercepts :

Find the $\"\"$ -intercept by substituting $\"\"$ in $\"\"$ .

$\"\"$

The $\"\"$ -intercept is $\"\"$ .

Find the $\"\"$ -intercept by substituting $\"\"$ in $\"\"$ .

$\"\"$

The $\"\"$ -intercept is $\"\"$ .

$\"\"$

Find the extrema of $\"\"$ .

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

$\"\"$

$\"\"$ .

Find the critical numbers by solving $\"\"$ .

$\"\"$ .

The first derivative is undefined at $\"\"$ .

$\"\"$ is not in the domain of the original function $\"\"$ .

Therefore, there is no relative extrema.

The function is always decreasing on its domain since $\"\"$ .

$\"\"$

Find the inflection points :

The first derivative of $\"\"$ is $\"\"$ .

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

$\"\"$

The second derivative of $\"\"$ is $\"\"$ .

Find the inflection points by solving $\"\"$ .

$\"\"$ .

The second derivative is undefined at $\"\"$ .

$\"\"$ is not in the domain of the original function $\"\"$ .

Therefore, there are no inflection points.

Check the concavity at undefined values.

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

\ \

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

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

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

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

$\"\"$

Find asymptotes of function $\"\"$ .

Find the horizontal asymptote by evaluating $\"\"$ .

$\"\"$

The horizontal asymptote is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

$\"\"$

$\"\"$ .

The vertical asymptote is $\"\"$ .

The horizontal asymptote is $\"\"$ .

$\"\"$

Graph the function $\"\"$ .

The domain of the function is all real numbers except $\"\"$ .

Intercepts are $\"\"$ and $\"\"$ .

The vertical asymptote is $\"\"$ .

The horizontal asymptote is $\"\"$ .

There is no relative extrema.

There are no inflection points.

Graph:

Draw the coordinate plane.

Plot the intercepts and asymptotes.

Connect the curve with plotted points.

Graph the function $\"\"$ :

$\"\"$

Graph of the function $\"\"$ .

$\"\"$ .