Not Every Forbidden Input Earns an Asymptote

You’ll learnto decide when a forbidden input produces a vertical asymptote and when it collapses to a hole.

A vertical asymptote is the graph losing its composure: outputs running off without bound as the input closes in on a value the function cannot accept. A shared factor changes everything, and counting copies casts the deciding vote. Twelve short steps; press Next for each one.

12 STEPS · 6 QUICK CHECKS · MULTIPLICITY TEST · ONE-SIDED LIMITS · FULL INVENTORY · v3

denominator wins → asymptote · numerator holds → hole

Before you start

What you're looking at

A table of outputs for 1/(x−2) as the input closes in on 2 from both sides.

The question

As the input approaches the forbidden value, do the outputs run off without bound?

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