Write the rational equation given the characteristics below. Leave in factored form.

Question

vertical asymptotes at x = − 6 and x = − 3

x -intercepts at x = − 4 and x = 3

horizontal asymptote at y = 4

Answer 1

For vertical asymptotes put (x+3)(x+6) in the denominator

For zeroes in y: put (x+4)(x-3) in the numerator

You can get a horizontal asymptote as x goes to +/- infinity by seeing that the limiting behavior is that the fraction goes to 1. So multiply by 4. This will not change any zeroes or vert. asymptotes.

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