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The function has a vertical asymptote of x=2 The function has a removable discontinuity of x=-2 The function has a horizontal asymptote of y= 0 No x intercept Y-intercept is (0,-0.5) End Behavior f(x) --> 0, x? -oo f(x) ? 0, x ? oo

What is the rational function? Please help!!
( ‘oo’ is infinity btw)

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1 answer

  1. come on, just follow the steps:
    vertical asymptote of x=2
    y = 1/(x-2)

    removable discontinuity of x=-2
    y = (x+2)/((x-2)(x+2))

    horizontal asymptote of y= 0
    no adjustment needed, since the degree below is greater than that above

    No x intercept
    still no adjustment needed, since everywhere except x = -2, y = 1/(x-2), which has no x-intercept.

    y-intercept is (0,-0.5)
    (x+2)/((x-2)(x+2)) = 2/-4 = -0.5 at x=0, so we are done.

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