Please help me solve

Question

Write an equation for a rational function with: Vertical asymptotes at x = 1 and x = 6 x intercepts at x = -6 and x = -1 y intercept at 8

Answer 1

Vertical asymptotes at x = 1 and x = 6 means the denominator is (x -1)(x - 6)

x-intercepts at x = -6 and x = -1 means numerator is (x + 6)(x + 1)

Using:

We can find the y-intercept by plugging in x = 0 and y = 8 and then solve for a:

8 = a(0 + 6)(0 + 1)/[(0 - 1)(0 - 6)]

8 = 6a/6

8 = a

Plug in a = 8 to the function above.