Reading Domain and Range off a Graph — Cheat sheet

CHEAT SHEET · FREE

Key method

Use brackets for included endpoints and parentheses for excluded endpoints. A missing point removes an output from the range only if no other point on the graph has that same height.

Example

Consider the line segment $y=2x+1$ for $-1<x\le2$ . Its horizontal projection is $(-1,2]$ . Since the line increases, its vertical projection is $(-1,5]$ . If a graph has a hole at $(0,1)$ but also passes through $(2,1)$ , the output $1$ still belongs to its range.

Avoid this mistake

Do not interpret the edge of a plotted window as a mathematical endpoint. Look for an explicit domain, endpoint marker or continuation arrow.