$\"\"$

The rational function is $\"\"$ .

The domain of a rational function is the set of all real numbers except those for

which the denominator is $\"\"$ .

Find which number make the fraction undefined create an equation where the

denominator is not equal to $\"\"$ .

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

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

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

$\"\"$ is in lowest terms is $\"\"$ .

The rational function is $\"\"$ .

Change $\"\"$ to $\"\"$ .

$\"\"$ .

Find the intercepts.

Find the $\"\"$ -intercept by equating $\"\"$ to zero.

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

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$\"\"$ -intercept is $\"\"$ and $\"\"$ -intercept is $\"\"$ .

Find the vertical asymptote by equating denominator to zero.

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

Find horizontal asymptote, first find the degree of the numerator and degree

of the denominator.

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 function has horizontal asymptote at $\"\"$ .

The zero of the numerator is $\"\"$ ; the zero of denominator is $\"\"$ ,

use these values to divide the $\"\"$ - axis into three intervals.

$\"\"$ .

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

Interval	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Number chosen \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Value of $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Location of graph \	\ Above $\"\"$ -axis \	\ Below $\"\"$ -axis \	\ Above $\"\"$ -axis \
\ Point of graph \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \

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Behavior of the graph:

$\"\"$ and $\"\"$ , hence the graph of $\"\"$ is

will approach the vertical asymptote, at $\"\"$ .

$\"\"$ and $\"\"$ , hence the graph of $\"\"$ is

will approach the horizontal asymptote, at $\"\"$ .

Graph:

The graph of $\"\"$ :

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$\"\"$ ; Domain of $\"\"$ is $\"\"$ .

$\"\"$ is in lowest terms.

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

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

Horizontal asymptote is $\"\"$ , not intersected. \ \

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

Interval	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Number chosen \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Value of $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \
\ Location of graph \	\ Above $\"\"$ -axis \	\ Below $\"\"$ -axis \	\ Above $\"\"$ -axis \
\ Point of graph \	\ $\"\"$ \	\ $\"\"$ \	\ $\"\"$ \

Graph of $\"\"$ :

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