Rational Function

Question

Write an equation for a rational function with:

Vertical asymptotes at x = -1 and x = -2

x-intercepts at x = 4 and x = 5

y-intercept at 3

Answer 1

y = (x-4)(x-5)/(x+1)(x+2)

with y intercept of 3 or the point (0,3)

3 = (-4)(-5)(1)(2) = 40 -37

subtract 37 from y

y = (x-4)(x-5)/(x+1)(x+2) -37

expand and collect like terms, if you want