pre cal

Find a possible formula for the function graphed below. The x-intercept is marked with a point located at (5,0), and the y-intercept is marked with a point located at (0,−0.833333333333333). The asymptotes are y=−1 and x=6. Give your formula as a reduced rational function.

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  1. vertical asymptote at x=6
    and a horizontal asymptote means
    y = a(x-b)/(x-6) + c

    y(5) = 0, so b=5

    y = a(x-5)/(x-6) + c

    y(0) = -5/6 and
    y(∞) = -1, so
    5/6 a + c = -5/6
    a + c = -1

    1/6 a = -1/6
    a = -1
    c = 0

    y = (5-x)/(x-6)

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