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

## Answer This Question

## Related Questions

- calculus - Leave any unneeded answer spaces blank. [Hint: use synthetic division...
- Calculus AB - Let f be the function that is given by f(x)=(ax+b)/(x^2 - c). It ...
- math - Explain why the graph of g(x) = 1/x has a horizontal asymptote. What is ...
- Algebra ll - Please help..I do not understand any of this... Analyze the graph ...
- Algebra - write an equation for a rational function that has a vertical ...
- math - Suppose the the limit as x approaches 6 to the left equals infinity. What...
- Calculus - If the graph of y = (ax - b)/(x - c) has a horizontal asymptote y=5 ...
- Precalculus - Write an equation for rational function with given properties. a...
- advance functions gr12 - write an equation for a rational function whose graph ...
- calculus - The Horizontal Assymptote for the graph of f(x) = (-6x3 +2x + 5)/(x3-...

More Related Questions