Mistake Master
Mistake Master · AP Precalculus · Unit 4 · Step-Through Animation
The Curve Is Whatever Survives the Filter
You'll learnto treat an equation in x and y as a filter that a point either passes or fails.
An equation in x and y is not a formula waiting to be evaluated; it is a filter on points, and whatever satisfies it is the curve. That definition never mentions functions, which is why a circle is a perfectly good graph, and why the vertical line test answers a much narrower question than it usually gets asked. Twelve short steps; press Next for each one.
Unit 4 is not assessed on the AP exam; schools include it where local requirements ask.
the curve is every point that satisfies the equation
Before you start
What you're looking at
A scatter of candidate points, each about to be tested against a circle's equation.
The question
Which of these points belong to the curve, and how would you decide?