R
Rishtaara
Algebra & Precalculus
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.