Question

Find a rational function that satisfies the given conditions. Answers may vary, but try to give the simplest answer possible:

Vertical asymptotes x = -4, x = 5;

x-intercept (-2, 0)

Answer 1

Try
f(x)=(x+2)/((x+4)(x-5))
the term x+2 will give a x-intercept at x=-2, the denominator gives vertical asymptotes at x=-4 and 5.
See http://i263.photobucket.com/albums/ii157/mathmate/rational.png