$\"\"$

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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 function is $\"\"$ .

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

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$\"\"$ .

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

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$\"\"$

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$\"\"$ $\"\"$

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$\"\"$ intercepts are $\"\"$ and $\"\"$ .

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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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$\"\"$ $\"\"$

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So the function has vertical asymptotes at $\"\"$ and $\"\"$ .

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Find the horizantal asymptote. \ \

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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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The ratio of the leading coefficients of numerator and denominator are equal,and the degree of polynomial are equal $\"\"$ is horizontal asymptote.

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

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The function is $\"\"$ .

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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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Therefore the function is undefined at the real zero of the denominator $\"\"$ .

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

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

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$\"\"$

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$\"\"$ intercepts are $\"\"$ and $\"\"$ .

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

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

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

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

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Graph of the function $\"\"$ is \ \

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$\"\"$