$\"\"$

The function is $\"\"$ .

Intercepts :

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

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The $\"\"$ -intercepts are $\"\"$ and $\"\"$ .

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

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

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Find the relative extrema for the function $\"\"$ :

Consider $\"\"$ .

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

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

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The solution of $\"\"$ are $\"\"$ and $\"\"$ in the interval $\"\"$ .

Thus, the critical points occur at $\"\"$ and $\"\"$ .

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

The relative maximum is $\"\"$ .

The relative minimum is $\"\"$ .

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Find the inflection points:

Consider $\"\"$ .

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

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The solutions of $\"\"$ are $\"\"$ and $\"\"$ in the interval $\"\"$ .

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

The inflection points are $\"\"$ , and $\"\"$ .

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Find the asymptotes :

The function is $\"\"$ .

There is no vertical asymptote for the function $\"\"$ .

Horizontal asymptote :

The line $\"\"$ is a horizontal asymptote if $\"\"$ .

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Limit does not exist.

Therefore, there is no horizontal asymptote for the function $\"\"$ .

$\"\"$

Find intervals of increase or decrease :

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

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

\ Interval \	Test Value	Sign of $\"\"$	Sign of $\"\"$	Conclusion
$\"\"$	$\"\"$	\ $\"\"$ \	\ $\"\"$ \	Decreases, point of inflection
$\"\"$	$\"\"$	$\"\"$	\ $\"\"$ \	\ Increases, point of inflection \
$\"\"$	$\"\"$	$\"\"$	\ $\"\"$ \	Decreases, concave downward

The graph is increases on the intervals $\"\"$ .

The graph is decreases on the interval $\"\"$ and $\"\"$ .

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Using all the above characteristics of the function, graph the function $\"\"$ in the interval $\"\"$ .

Graph :

Draw a coordinate plane.

Graph the function $\"\"$ in the interval $\"\"$ .

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The function is $\"\"$ in the interval $\"\"$ .

Graph :

Using the graphing utility draw the the graph of the function $\"\"$ in the interval $\"\"$ .

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Observe the above two graphs : The graphs represents the same function, i.e, $\"\"$ .

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Graph of the function $\"\"$ in the interval $\"\"$ :

$\"\"$ .