Translations and reflections

Translations and reflections of function graphs

Learn to track what happens to both coordinates when a function moves or reflects. This precalculus practice set connects symbolic rules with points, intervals and timing models, giving meaning to the signs inside and outside a function argument.

Begin with horizontal and vertical shifts, then distinguish reflections across the horizontal and vertical axes. Work with translated square-root functions, open and closed domain endpoints, reflected ranges and the original coordinates of a transformed point. A short data table supports reverse construction, while a timing context tests whether a delayed event calls for an earlier or later input to the original rule.

Before starting, review algebraic parent functions, function notation and interval notation. Try solving the input equation instead of relying solely on a left-right mnemonic. The more demanding items compare transformation sequences and use a counterexample to diagnose an incorrect sign choice.

Single-select and multiselect questions progress from direct coordinate changes to explanation and reconstruction. Detailed solutions show which coordinate changes, which stays fixed and how to check the result. General horizontal and vertical scaling is reserved for the next topic; this set concentrates on translations and reflections.