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).

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.

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

is this correct?

Correct.

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

To find a formula for the rational function g(x) given the information provided, we can start by identifying the key components of the function based on the given asymptotes and zeros.

1. Vertical Asymptotes: The vertical asymptotes of g(x) occur when the denominator of the rational function is zero. From the given information, we know that the lines x = 2 and x = -2 are the vertical asymptotes. Therefore, the denominator must include factors of (x - 2) and (x + 2).

2. Zeros: We are given that the function g(x) has zeros at x = 3 and x = 1. This means that the numerator of the rational function must have factors of (x - 3) and (x - 1).

3. Horizontal Asymptote: The line y = 4 is the horizontal asymptote of g(x). This implies that as x approaches positive or negative infinity, the function approaches the value of 4. Therefore, the degree of the denominator should be equal to or greater than the degree of the numerator.

Based on the above analysis, we can write the formula for the rational function g(x) as follows:

g(x) = (x - 3)(x - 1) / [(x - 2)(x + 2)]

The numerator (x - 3)(x - 1) captures the zeros at x = 3 and x = 1, while the denominator (x - 2)(x + 2) accounts for the vertical asymptotes at x = 2 and x = -2. Since the degree of the numerator (2) is less than the degree of the denominator (2), the horizontal asymptote at y = 4 is satisfied.

Note: If there are additional requirements or constraints not mentioned in the question, the formula could be adjusted accordingly.