rational equations

Question

Write an equation for a rational function with:

Vertical asymptotes at x = 3 and x = 1

x intercepts at x = -1 and x = -6

y intercept at 10

Answer 1

Vertical asymptotes mean we need to have (x-3)(x-1) in the denominator.

x-intercepts mean we need to have (x+1)(x+6) in the numerator.

So thus far, this is what we have for the function:

f(x) = (x+1)(x+6)/((x-3)(x-1))

Multiplying out, we have:

f(x) = (x²+7x+6)/(x²-4x+3)

To accommodate the y-intercept, we need to find out the current y-intercept:

f(0) = 6/3

To make the y-intercept equal to 10, we need to add 24/3 to the function. So the final function is:

f(x) = (x²+7x+6)/(x²-4x+3) + 24/3