Final answer:
A simple example of a rational function with vertical asymptotes at x=-2 and x=6 is f(x) = 1/((x+2)(x-6)). The numerator of the function can be any non-zero polynomial, which will not alter the location of the vertical asymptotes.
Step-by-step explanation:
To write the equation of a rational function with specified vertical asymptotes, we need to include factors in the denominator that will become zero at those asymptote values. Vertical asymptotes at x=-2 and x=6 imply that the rational function will have factors of (x+2) and (x-6) in the denominator, since setting these factors to zero gives us the asymptote values.
An example of such a rational function could be:
f(x) = √ rac{1}{(x+2)(x-6)}
This is the simplest form of a rational function with the given vertical asymptotes. However, you can multiply the numerator by any non-zero polynomial to get different rational functions that still satisfy the condition of having vertical asymptotes at x=-2 and x=6.