AP Calculus AB and BC glossary

One-to-one function

Also called: Injective function

A function is one-to-one when different inputs always give different outputs, which is what the horizontal line test checks. Only a one-to-one function has an inverse, and any strictly increasing or strictly decreasing function is automatically one-to-one.

This is why inverse function problems restrict the domain. Sine is not one-to-one on the whole line, so arcsine is defined using only a restricted piece of it.

The mistake

Using the vertical line test. That checks whether a relation is a function at all; the horizontal line test is what checks invertibility.

Appears in: Unit 3: Chain Rule, Implicit, and Inverses