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calculus

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f(x)= (5x^4 + 5x^3 + 6x^2 + 8x + 5)/(1x^4 + 1x^3 + 1x^2 - 9x + 4)

What is the equation of the horizontal asymptote? y = ___?

Does the graph of f(x) intersect its horizontal asymptote? (yes or no)

If yes, at what x-values does f(x) intersect its horizontal asymptote? Give your answers in increasing order. ___, ___.

  • calculus - ,

    hor. asymp: just divide highest powers
    5x^4/1x^4 = 5, so y=5

    Rational functions almost always intersect the hor. asymp. Since the denominator here has two real roots, there will be two vertical asymptotes.
    Since there are no double roots, the graph goes to infinity in both + and - directions. Since f(x) < 5 for x--> -∞, but f(x)>5 for x near .5, the graph crosses the asymptote.

    In fact, it crosses at x = -53.28 and 0.28

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