$\"\"$

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The rational function is $\"\"$ .

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The function can be written as $\"\"$ .

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Find the intercepts.

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The rational function is $\"\"$ .

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

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$\"\"$ .

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$\"\"$ .

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

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$\"\"$

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$\"\"$ intercept is $\"\"$ .

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

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$\"\"$

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

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Find the vertical Asymptotes.

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Find the vertical asymptotes by equating denominator to zero.

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$\"\"$

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

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Find the horizantal asymptotes :

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

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

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degree of the denominator is greater than the degree of the numerator.

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Therefore Horizantal asymptote is $\"\"$ .

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

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The rational function is $\"\"$ .

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There is a hole at $\"\"$ because the original function is undefined when $\"\"$ .

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Graph :

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Draw the coordinate plane.

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Graph the function $\"\"$ .

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$\"\"$

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Find the domain :

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The function is $\"\"$ .

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The domain of a function is the set of all real numbers which makes the function mathematically correct.

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Denominator of the function should not be $\"\"$ .

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$\"\"$

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Thus, the function is continuous for all real numbers except $\"\"$ .

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Therefore, domain of the function is $\"\"$ .

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$\"\"$

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$\"\"$ intercept is $\"\"$ .

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

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

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

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Domain of the function is $\"\"$ .

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Graph the function $\"\"$ . \ \

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$\"\"$