$\"\"$

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Observe the graph :

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$\"\"$ intercepts :

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The $\"\"$ intercept of the rational function are $\"\"$ .Since $\"\"$ is a $\"\"$ intercept, $\"\"$ is a factor of the numerator.

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In the graph there appears another $\"\"$ intercept, Let the other intercept be $\"\"$ ,which is the second

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$\"\"$ intercept, $\"\"$ is a factor of the numerator.

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Vertical Asymptotes :

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The rational function has vertical asymptotes at $\"\"$ and $\"\"$ , therefore the zeros of the denominator should not be $\"\"$ and $\"\"$ .

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

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Horizantal Asymptote :

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Because there is a horizontal asymptote at $\"\"$ , the degrees of the polynomials in the numerator and denominator are equal and the ratio of their leading coefficients is $\"\"$ .

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Point :

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Observe the graph the point is $\"\"$ .

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The equation that satisfies all the above characterictics is $\"\"$ .

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$\"\"$

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Subustiute the points $\"\"$ in the obtained equation $\"\"$ and solve for $\"\"$ . Here $\"\"$ .

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$\"\"$

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$\"\"$

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Subustiute the value of $\"\"$ in the original equation $\"\"$ .

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$\"\"$

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The rational function that represents the graph is $\"\"$ .

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$\"\"$

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The rational function that represents the graph is $\"\"$ .