Question

Write an equation for a rational function whose graph has the following properties:

x-intercept of 3 y-intercept of -3
vertical asymptote of x=-2
horizontal asymptote of y=2

Answer 1

x-intercept of 3 ---> needs a multiplier of x-3
vertical asymtote of x = -2 ----> needs a divisor of x+2

so far y = (x-3)/(x+2)

horizontal asymptote of y = 2
lets slap a 2 infront

y = 2(x-3)/(x+2) , as x gets huge y ---> 2 , ( try x = 100,000 )

we want y-intercept of -3, (when x = 0)
We lucked out, since if x = 0 , y = -6/2 = -3

y = 2(x-3)/(x+2)