Rational Functions & Graphs

Question

Write an equation for a rational function with:

Vertical asymptotes at  and 

 intercepts at  and 

Horizontal asymptote at 

Answer 1

Vertical asymptotes result from a denominator equal to zero. So the denominator must include (x + 6) and (x + 3).

x-intercept are found when the numerator equals zero so the numerator must include (x + 2) and (x - 2).

So far we have f(x) = [(x + 2)(x - 2)]/[(x + 6)(x + 3)]

Both numerator and denominator have the same degree so the horizontal asymptote will be the leading coefficient of the numerator divided by the leading coefficient of the denominator. We can get a horizontal asymptote at y = 3 by just multiplying the numerator by 3. So: