Question

Give an example of a rational function that has vertical asymptote x = 3 and x = -3, horizontal asymptote y = 2 and y-intercept is (0, 4)

Answer 1

f(x) = (x-4)/(x^2-9) + 2

Answer 2

Hmmm. f(0) = -4/-9 + 2 ≠ 4

How about

y = -18/(x^2-9) + 2 = 2(x^2-18)/(x^2-9)

That also has two x-intercepts. If you don't want any of those, then you will need to have y>0 for all x.

y = 2*9^2/(x^2-9)^2 + 2