# Calculus

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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 -

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.

• Calculus -

So i got g(x)= (4x^2-16x+12)/(x^2-4)
is this correct?

• Calculus -

Correct.
For you reference, see:
http://img94.imageshack.us/img94/1728/1283787460.png

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