$\"\"$

The function is $\"\"$ .

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

Intercepts:

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

$\"\"$

Since the equation has no real solutions, there are no $\"\"$ -intercepts.

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 $\"\"$ .

$\"\"$ .

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

$\"\"$ .

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

Relative maximum at $\"\"$ .

The critical numbers are $\"\"$ .

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

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

\ \

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

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

$\"\"$

Find the points of inflection.

$\"\"$

$\"\"$ .

$\"\"$

$\"\"$ .

Equate $\"\"$ to $\"\"$ .

$\"\"$

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

Therefore, there is no inflection points.

Check the concavity at undefined values.

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

\ \

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

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

$\"\"$

Find asymptotes of function $\"\"$ .

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

$\"\"$

Substitute As $\"\"$ Then $\"\"$ .

$\"\"$

The horizontal asymptote is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

$\"\"$

The vertical asymptote are at $\"\"$ and $\"\"$ .

$\"\"$

Graph the function $\"\"$ .

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

There is no intercepts.

Vertical asymptotes are at $\"\"$ .

The horizontal asymptote is $\"\"$ .

Relative maximum at $\"\"$ .

There is no inflection points.

Graph:

Draw the coordinate plane.

Plot the asymptotes and local minimum.

Connect the curve with plotted points.

Graph of the function $\"\"$ .

$\"\"$

Graph of the function $\"\"$ .

$\"\"$ .