Posted by **Leanna** on Monday, September 6, 2010 at 11:37am.

A rational function g has the lines x=2 and x=-2 as vertical asymptotes, the line y=4 as a horizontal asymptote, and numbers 3 and 1 as zeros. Find a formula for g(x).

- Calculus -
**MathMate**, Monday, September 6, 2010 at 1:11pm
With x=2 and x=-2 as vertical asymptotes, the denominator of g(x) contains the factors (x-2) and (x+2).

To get 3 and 1 as zeroes, the numerator must contain the factors (x-3) and (x-1).

The horizontal asymptote of y=4 implies that lim x->∞ and x->-∞ g(x) = 4. This is the case when the highest powered term of the numerator divided by the highest power term of the denominator is 4.

Find g(x), and plot the graph to verify your answer.

- Calculus -
**Leanna**, Monday, September 6, 2010 at 6:50pm
So i got g(x)= (4x^2-16x+12)/(x^2-4)

is this correct?

- Calculus -
**MathMate**, Monday, September 6, 2010 at 7:46pm
Correct.

For you reference, see:

http://img94.imageshack.us/img94/1728/1283787460.png

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