$\"\"$

The function is $\"\"$ .

The domain of the function is all real numbers.

Intercepts:

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

$\"\"$

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

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

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

$\"\"$

Find the extrema of $\"\"$ .

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

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$\"\"$ .

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

$\"\"$ .

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$\"\"$ or $\"\"$

The critical points are $\"\"$ , $\"\"$ .

Relative extrema points exist at critical numbers.

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

Maximum is at $\"\"$ and minimum at $\"\"$ .

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

\ \

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

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

$\"\"$

Find the inflection points.

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

$\"\"$ .

$\"\"$

$\"\"$ .

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

$\"\"$ .

$\"\"$

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

The inflection points occurs at $\"\"$ , $\"\"$ and $\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$ .

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

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

\ \

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

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

$\"\"$

Find asymptote of function $\"\"$ .

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

$\"\"$

Take common numerator and denominator by $\"\"$ .

$\"\"$

The horizontal asymptote is $\"\"$ .

Find the vertical asymptotes by equating denominator to zero.

$\"\"$

Since the equation has no real solutions, there are no vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

The domain of the function is all real numbers.

Intercept is $\"\"$ .

There is no vertical asymptote.

The horizontal asymptote is $\"\"$ .

Maximum is at $\"\"$ and minimum at $\"\"$ .

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

Graph:

Draw the coordinate plane.

Plot the intercepts, asymptote, maximum, minimum and inflection points.

Connect the curve with plotted points.

Graph of the function $\"\"$ :

$\"\"$

Graph of the function $\"\"$ :

$\"\"$ .