$\"\"$

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The $\"\"$ intercepts of the rational function are $\"\"$ and $\"\"$ .

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Vertical asymptotes are at $\"\"$ .

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Points of discontinuity at $\"\"$ .

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$\"\"$ Intercepts :

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The rational function has $\"\"$ intercepts at $\"\"$ and $\"\"$ , therefore the zeros of numerator are $\"\"$ and $\"\"$ .

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Therefore the factors of the numerator are $\"\"$ and $\"\"$ .

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Vertical Asymptotes :

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The rational function has vertical asymptotes at $\"\"$ , therefore the zero of the denominator needs to be $\"\"$ .

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Therefore the factor of the denominator is $\"\"$ .

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Points of discontinuity :

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Points of discontinuity at $\"\"$ .

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For there to be point discontinuity at $\"\"$ , $\"\"$ must be a factor of both the numerator and denominator.

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The point of discontunity at $\"\"$ the numerator must have a $\"\"$ at $\"\"$ .

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Thus, the $\"\"$ in the numerator must have a power of $\"\"$ so that $\"\"$ remains a $\"\"$ of the numerator after the function is simplified.

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Rational Function :

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Therefore the rational function is $\"\"$ .

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$\"\"$

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The rational function is $\"\"$ .