A Puncture, Not a Wall

You'll learnto tell a removable hole from a vertical asymptote in a rational function.

Both a hole and a vertical asymptote sit at an input the function refuses. One is repairable with a single dot and the other tears the graph in two, and the difference is decided entirely by whether the shared factors cancel.

8 STEPS · 6 QUICK CHECKS · HOLES · ASYMPTOTES · DOMAIN DEBTS · v3

shared and cancelling gives a hole; unshared gives a wall

Before you start

What you're looking at

The line y = x + 2 with a single point punched out at (2, 4).

The question

What is different about this graph — and why does one missing dot count?

Watch for

Whether the shared factor cancels (a hole) or not (a wall), with the excluded input marked throughout.

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