$\"\"$

The function is $\"\"$ .

Intercept:

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

$\"\"$

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

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

$\"\"$

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

$\"\"$

Find the extrema for $\"\"$ .

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

$\"\"$ .

$\"\"$

$\"\"$ .

To find the critical numbers we make $\"\"$ .

$\"\"$ .

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

The critical numbers are $\"\"$ and $\"\"$ .

$\"\"$

Find the points of inflection.

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

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

$\"\"$ .

$\"\"$

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

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

$\"\"$ .

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

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

$\"\"$

The critical numbers is $\"\"$ , $\"\"$ .

Relative extrema points exist at critical numbers.

Substitute $\"\"$ in the function.

$\"\"$

$\"\"$ .

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
$\"\"$	\ $\"\"$ \	Relative minimum

Relative minimum point is $\"\"$ .

$\"\"$

Find asymptote of function $\"\"$ .

To find horizontal asymptote $\"\"$ .

$\"\"$ .

$\"\"$

There is no horizontal asymptote

To find vertical asymptote, denominator of the functionis equates to zero.

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

There is no vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

$\"\"$

Observe the graph ,

The intercepts are $\"\"$ , $\"\"$ .

Relative minimum point is $\"\"$ .

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

There is no horizontal and vertical asymptote.

$\"\"$

Graph the function $\"\"$ .

$\"\"$ .