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 .

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Rewrite the expression.

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is in lowest terms.

The rational function is .

Change to .

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Find the intercepts.

To find -intercept equate numerator .

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Therefore there is no -intercept in given function .

Find the -intercept by substituting in the rational function.

- intercept is .

Find the vertical asymptote by equating denominator to zero.

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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 is zero and degree of the denominator is .

Since the degree of numerator is less than degree of denominator,

so is a proper rational function, and the graph of will have the

horizontal asymptote .

The function has horizontal asymptote at .

There are no zeros of numerator; the zeros of denominator are ,

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

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End behavior of the graph:

As and , hence the graph of approaches

to a vertical asymptote at .

As and , hence the graph of approaches

to a vertical asymptote at .

As and , hence the graph of approaches

to a horizontal asymptote at .

Graph :

The graph of :

Step 1: ; Domain of function is .

Step 2: The function in lowest terms .

Step 3: There is no -intercepts and -intercept is .

Step 4: is in lowest terms.

Vertical asymptote at and .

Step 5: Horizontal asymptote is ; not intersected.

Step 6:

Step 7 and step 8:

Graph of :