Algebraic parent functions

Algebraic parent functions: graphs, domains and ranges

Build a working toolkit for precalculus by connecting the constant, identity, square, cube, square-root, cube-root, absolute-value and reciprocal functions with their graphs and input-output behavior. Coordinate diagrams, numerical values and short contextual problems invite you to identify a function from evidence rather than memorize a silhouette.

This practice set begins with graph recognition and develops comparisons of natural real domains, attainable outputs and behavior at negative inputs. Later questions ask you to distinguish formulas that agree at a few points, explain when two parent rules coincide and separate a mathematical domain from the physically meaningful inputs of a model.

You should be comfortable plotting ordered pairs, evaluating powers and roots, and reading interval notation. Work out the relevant coordinates or restrictions before selecting an answer. Both single-select and multiselect items include worked explanations that address common confusions, especially square versus absolute value, cube versus cube root, and zero as an excluded reciprocal input.

The focus is the algebraic toolkit. Exponential, logarithmic and trigonometric parents belong to later modules. Use this set to prepare for translations, reflections and scaling; it is topic practice, not a comprehensive placement assessment.