Mistake Master
Mistake Master · AP Precalculus · Unit 1 · Step-Through Animation
A Gap Exactly One Point Wide
You'll learnto tell a hole from a vertical asymptote, and to read the hole’s two coordinates.
A rational function can refuse an input in two very different ways. Sometimes the graph is torn in half; sometimes only a single point is missing. Which one you get is decided by whether the shared factors cancel. Twelve short steps; press Next for each one.
shared factors cancel to a hole · a lone factor below makes a wall
Before you start
What you're looking at
The line y = x + 2 with a single point lifted out at (2, 4).
The question
Why is one excluded input just a missing dot while another tears the graph?