$\"\"$

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The rational 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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Apply the zero product property.

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

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

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

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

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$\"\"$

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

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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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Thus, the function has vertical asymptote at $\"\"$ .

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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 is $\"\"$ and degree of the denominator is $\"\"$ .

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Here the degree of the numerator is greater than denominator, so the function will have oblique asymptote.

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Find oblique asymptote by long division.

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$\"\"$

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$\"\"$

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Here quotient is $\"\"$ .

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Oblique asymptote is $\"\"$ .

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Graph the function $\"\"$ . \ \ Draw a coordinate plane.

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Plot the intercepts and asymptotes.

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Draw the curve.

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Graph of the function $\"\"$ :

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$\"\"$

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Observe the graph of the function : The function is undefined at $\"\"$ .

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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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Vertical asymptotes at $\"\"$ .

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Oblique asymptote is $\"\"$ .

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The $\"\"$ -intercepts are $\"\"$ 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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$\"\"$ .