Question

Find an equation for the rational function which has a zero at x=6, a hole at x=3, and asymptotes at x=4 and y=5

Answer 1

vertical asymptote at x=4 so denominator must have factor (x-4)

Answer 2

hole at x=3, so must contain factor (x-3) on top and bottom such that they cancel

Answer 3

horizontal asymptote at y=5, so degree on top/bottom must be equal and ratio of leading coefficients must be 5
\[f(x) = \frac{5(x-a)(x-3)}{(x-3)(x-4)}\]

Answer 4

f(6) = 0 you can solve for variable "a"

Answer 5

Thanks that's what I got just was making sure someone else got the same answer as me. I appreciate it! :)

Answer 6

yw :)