FInding The Equation of a Rational Function

Question

A zero at x = 3

A hole when x = 5

A vertical asymptote at x = -1

A horizontal asymptote at y = 3

A y-intercept at y = -9

What is the equation of the rational fn?

Answer 1

f(x) = (3(x-3)(x-5))/((x-5)(x+1))

A zero (x-int) is a zero of the numerator only.

A hole (removable discontinuity) is a zero of both numerator AND denominator.

A vertical asymptote is a zero of the denominator only.

A horizontal asymptote will occur at y = ratio of the lead coefficients, when degrees are = in num and denom.

To give it the correct y-int, plug in x = 0 and evaluate. Add a constant, if necessary. (It wasn't here.)