$\"\"$

The rational function is $\"\"$ .

In rational functions the denominator can not be zero.

To find exceptional values equate denominator to zero.

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

$\"\"$ .

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$\"\"$ is in lowest terms.

The rational function is $\"\"$ .

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

$\"\"$ .

Find the intercepts.

To find $\"\"$ intercept equate numerator to $\"\"$ .

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

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

Find the vertical asymptote by equating denominator to zero.

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So the function has vertical asymptote at $\"\"$ .

To find horizontal asymptote, first find the degree of the numerator and degree of the denominator.

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

Oblique asymptote :

If the degree of the numerator is grater than the degree of denominator then

Oblique asymptote exist.

Thus, the function has no oblique asymptote.

The horizontal asymptote is $\"\"$ .

Graph :

Graph the function with its horizontal and vertical asymptotes.

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The zeros in the numerator is $\"\"$ and $\"\"$ .

The zeros of denominator are $\"\"$ and $\"\"$ , use these values to divide the $\"\"$ axis into three intervals.

$\"\"$ .

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End behavior of the graph:

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

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Graph :

The graph of $\"\"$ :

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The graph rational function $\"\"$ :

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