Lesson 3 of 12Article18 min
Functions: Domain, Range & Transformations
f: D → R maps each x in the domain to exactly one y. Vertical line test on a graph: a vertical line hits the graph at most once.
Function language
f: D → R maps each x in the domain to exactly one y. Vertical line test on a graph: a vertical line hits the graph at most once.
- Domain restrictions: division by zero, even roots of negatives, log of non-positives.
- Range: set of actual outputs — read from graph or complete the square.
- One-to-one: horizontal line test; invertible on a suitable domain.
Graph transformations
Apply horizontal changes to x inside first, then vertical changes outside.