Question

How do you find vertical, horizontal and oblique asymptotes for `y= (x^2 - 9)/(x-3)`?

Answer 1

First, factor the numerator: `y = ((x+3)(x-3))/(x-3)`

Explanation:

Cancel the factor `x-3` from both the numerator and denominator. You are left with `y = x+3`, a linear function!

The factor that was cancelled leaves a "hole" or removable discontinuity in your graph at x = 3.

If you plot the line `y = x+3`, there will be NO asymptotes at all, but just a little hole at the point (3,6).