Relations, functions and notation

Relations, functions and function notation

Build the central language of precalculus by deciding when a relationship assigns exactly one output to every allowed input. This practice set moves among mappings, recorded pairs, formulas, a coordinate graph and verbal descriptions. You will distinguish input-output notation from multiplication and learn why repeated outputs can still define a function.

Questions address incomplete assignments on a declared domain, repeated records, square-root branches and the vertical-line test. A graph task asks you to interpret the plotted relation itself. The focus is the meaning of a function; later lessons develop evaluation techniques, domain algebra, transformations and inverses in more detail.

Prerequisites and practice

Know ordered pairs, simple coordinate graphs and elementary algebraic notation. Begin by identifying the input and the allowed inputs, then check whether each receives a unique output. Work out your decision before comparing choices. Both single-select and select-all questions include explanations that diagnose plausible mistakes.

Use the feedback

Explain why a rejected relationship fails the definition, or why a valid relationship survives a suspected problem. A repeated output, an unfamiliar formula or an absent algebraic formula is not by itself a reason to reject a function.