Homework Help: calculus

Posted by gloria on Sunday, June 3, 2012 at 4:02am.

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 - Steve, Sunday, June 3, 2012 at 6:11am
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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