ACT Preparation / Unit 11 ACT 1026 short lesson, about 20 seconds
Vertical Asymptotes and Holes
Captions available
The idea
For a rational function, factor and cancel first. A factor that cancels leaves a hole at its zero; a zero of the reduced denominator gives a vertical asymptote.
In practice
f(x) = (x − 2)/((x − 2)(x + 3)) has a hole at 2 and a vertical asymptote at x = −3.
Where people slip
Neither 2 nor −3 is in the domain.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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