$\"\"$

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The rational function is $\"\"$ .

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Finding the intercepts :

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The function is $\"\"$ .

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

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$\"\"$ .

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Find the intercepts.

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

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

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

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

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$\"\"$

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

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Finding the vertical asymptotes :

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Find the vertical asymptote by equating denominator to zero.

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

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

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Finding 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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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.

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Leading coefficient of numerator $\"\"$ , leading coefficient of denominator $\"\"$ .

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$\"\"$ is horizontal asymptote.

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

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Graph :

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The graph of the function $\"\"$ .

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$\"\"$

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Find the domain :

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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 a function should not be $\"\"$ .

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To find which number make the fraction undefined create an equation where the denominator is not equal to $\"\"$ .

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

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

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Therefore domain $\"\"$ .

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$\"\"$

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Domain $\"\"$ .

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

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

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The graph of the function is

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$\"\"$