$\"\"$

The function is $\"\"$ .

The domain of the function is all real numbers.

Intercepts:

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

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

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

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

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Find the extrema of $\"\"$ .

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

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

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Relative extrema points exist at critical numbers.

Substitute $\"\"$ in the function.

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Relative minimum is at $\"\"$ .

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

\ \

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

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

$\"\"$

Find the inflection points.

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$\"\"$ .

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

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

Substitute $\"\"$ in the function.

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$\"\"$ .

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

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

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

\ \

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

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

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Find asymptotes of function $\"\"$ .

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

$\"\"$

The horizontal asymptote is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

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The vertical asymptote is $\"\"$ .

$\"\"$

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

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Graph the function $\"\"$ .

The domain of the function is all real numbers.

Intercept is $\"\"$ .

There is no vertical asymptote.

The horizontal asymptote is $\"\"$ .

Minimum is at $\"\"$ .

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

Graph:

Draw the coordinate plane.

Plot the intercepts, asymptote, minimum and inflection points.

Connect the curve with plotted points.

Graph of the function $\"\"$ :

$\"\"$

Graph of the function $\"\"$ :

$\"\"$ .