Write an equation for a rational function

Question

Vertical asymptotes at x=2 and x=1

x intercepts at x=6 and x=3

y intercept at 3

Answer 1

The vertical asymptotes at 2 and 1 mean there are zeroes in the denominator: 1/((x-2)(x-1))

The x intercepts at 6 and 3 mean there are zeros in the numerator: ((x-6)(x-3))/((x-2)(x-1))

The y intercept at 3 means that when we plug in 0 for x, we need to get an answer of 3.

((-6)(-3))/((-2)(-1)) = 18/2 = 9.

Since we need to get 3 instead of 9 for this value, we're going to divide by 3. Our final answer is then:

((x-6)(x-3))/(3(x-2)(x-1))