Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = -5 x intercepts at x = 1 and x = -3 y intercept at 10

Question

Write an equation for a rational function with:

Vertical asymptotes at x = 4 and x = -5

x intercepts at x = 1 and x = -3

y intercept at 10

Answer 1

From the vertical asymptotes and zeroes listed, we get

f(x) = a(x-1)(x+3)/(((x-4)(x+5))

y-intercept at 10 means that f(0) = 10

Then, 10 = a(-1)(3)/((4)(-5))= 3/20 a

3/20 a = 10, so a = 10 / (3/20)) = 200/3

f(x) = 200(x-1)(x+3)/(3(x-4)(x+5))