$\"\"$

The rational function is $\"\"$ .

Factorize the numerator and denominator.

$\"\"$

$\"\"$ .

The domain of the function is all possible values of $\"\"$ .

The denominator of the function should not be zero.

$\"\"$

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

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

The domain of the $\"\"$ is the set of all real numbers $\"\"$ except $\"\"$ and $\"\"$ .

The domain of function $\"\"$ is $\"\"$ .

$\"\"$ .

There are no common factors between the numerator and denominator, $\"\"$ is in lowest terms.

The rational function is $\"\"$ .

Find the intercepts.

Find the $\"\"$ -intercepts by equating $\"\"$ .

$\"\"$

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

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

$\"\"$ -intercepts: $\"\"$ .

Determine the behavior of the graph of $\"\"$ near each $\"\"$ -intercept.

Near $\"\"$ : $\"\"$ .

Plot the point $\"\"$ and indicate a line with negative slope.

Near $\"\"$ : $\"\"$ .

Plot the point $\"\"$ and indicate a line with positive slope.

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

$\"\"$

$\"\"$ .

$\"\"$ -intercept: $\"\"$ .

The rational function is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

$\"\"$

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

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

The function has vertical asymptote $\"\"$ and $\"\"$ .

Find the horizontal or oblique asymptote.

$\"\"$ .

Degree of the numerator is $\"\"$ and degree of the denominator is $\"\"$ .

Since the degree of the numerator is equal to the degree of the denominator, horizontal asymptote is the ratio of leading coefficient of numerator and denominator.

Leading coefficient of numerator is $\"\"$ , leading coefficient of denominator is $\"\"$ .

$\"\"$ is horizontal asymptote.

$\"\"$

The oblique asymptote intersected the graph at $\"\"$ .

$\"\"$

The zeros of the numerator are $\"\"$ ; the zeros of the denominator are $\"\"$ .

Use these values to divide the $\"\"$ axis into five intervals.

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

$\"\"$

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

Interval	\ $\"\"$ \	\ $\"\"$ \	Location of graph	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
\ $\"\"$ \	\ \ $\"\"$ \	\ \ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ Below \ $\"\"$ -axis \	\ $\"\"$ \
$\"\"$	\ $\"\"$ \	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
$\"\"$	$\"\"$	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \

$\"\"$

End behavior of the graph:

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

$\"\"$

Graph :

The graph of $\"\"$ :

$\"\"$

Step 1: $\"\"$ . The Domain of $\"\"$ is $\"\"$ .

Step 2: $\"\"$ is in lowest terms.

Step 3: $\"\"$ intercept: $\"\"$ ; $\"\"$ -intercepts: $\"\"$ .

Step 4: $\"\"$ is in lowest terms; vertical asymptotes: $\"\"$ and $\"\"$ .

Step 5: Horizontal asymptote is $\"\"$ , intersected at $\"\"$ .

Step 6:

$\"\"$

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

Interval	\ $\"\"$ \	\ $\"\"$ \	Location of graph	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
\ $\"\"$ \	\ \ $\"\"$ \	\ \ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
$\"\"$	\ $\"\"$ \	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \
$\"\"$	$\"\"$	\ $\"\"$ \	\ Above \ $\"\"$ -axis \	\ $\"\"$ \

Step 7 and step 8:

The graph of $\"\"$ .

$\"\"$ .