Homework help!

Question

What is a rational function with a vertical asymptote at X=6, x=-2, with a zero at X=3?

I seem to be stuck on this problem and would love some help.

Answer 1

There are many rational functions that satisfy these conditions.  A simple example:

 

Make the numerator x - a, where a is the zero.  Make the denominator (x - b)(x - c), where b and c are where the vertical asymptotes cross the x-axis.

 

f(x) = (x - 3) / [(x - 6)(x + 2)]