$\"\"$

The function is $\"\"$ .

Intercept :

To find the $\"\"$ -intercept substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

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

To find the $\"\"$ -intercept, substitute $\"\"$ in the function.

$\"\"$

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

$\"\"$

Find the extrema for $\"\"$ .

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

$\"\"$ .

Power rule of derivatives : $\"\"$ .

$\"\"$

$\"\"$ .

Find the critical numbers by equating $\"\"$ to $\"\"$ .

$\"\"$ .

The critical numbers are $\"\"$ .

$\"\"$

Find the points of inflection.

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

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

$\"\"$ .

Power rule of derivatives : $\"\"$ .

$\"\"$

$\"\"$ .

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

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

$\"\"$ .

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

$\"\"$

The critical numbers is $\"\"$ .

Relative extrema points exist at critical numbers.

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

Perform second derivative test to identify the nature of the extrema.

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

Test value	Sign of $\"\"$	Conclusion
$\"\"$	\ $\"\"$ \	Test fails

No relative extrema.

$\"\"$

Find asymptote of function $\"\"$ .

To find horizontal asymptote $\"\"$ .

$\"\"$ .

There is no horizontal asymptote.

To find vertical asymptote,equate denominator to zero.

The function is defined for all values of $\"\"$ .

There is no vertical asymptote.

$\"\"$

Graph :

Graph the function $\"\"$ .

$\"\"$

Observe the graph ,

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

No relative extrema.

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

There is no horizontal and vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

$\"\"$