$\"\"$

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The rational function is $\"\"$ .

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Domain of the function :

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To find the excetional values equate denominator to zero.

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$\"\"$

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$\"\"$

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$\"\"$ , $\"\"$ and $\"\"$

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

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

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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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Find $\"\"$ -intercept by equating the numerator to zero.

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$\"\"$

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

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

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$\"\"$ is not in the domain of the function. \ \

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The $\"\"$ -intercepts is $\"\"$ .

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Find $\"\"$ -intercept by substituting $\"\"$ in $\"\"$ .

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$\"\"$

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There is no $\"\"$ -intercept because $\"\"$ is undefined.

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Find the vertical asymptotes :

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Find the vertical asymptote by equating the denominator to zero.

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$\"\"$

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$\"\"$

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$\"\"$ , $\"\"$ and $\"\"$

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

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Thus, the function has vertical asymptote 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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Since the degree of numerator is less than the degree of the denominator, the function has horizontal asymptote, at $\"\"$ .

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Draw a coordinate plane.

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Graph the function $\"\"$ .

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Graph :

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$\"\"$ \ \

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Observe the graph :

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Find the domain :

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The function is undefined at $\"\"$ , $\"\"$ and $\"\"$ . \ \

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

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$\"\"$

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Horizontal asymptote at $\"\"$ .

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Vertical asymptotes at $\"\"$ and $\"\"$ .

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

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Domain : $\"\"$ .

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Graph of the function $\"\"$ :

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$\"\"$ .