Optional prior-learning diagnostic

This optional precalculus diagnostic is intended for learners who have already studied functions, graphs, exponential models or elementary trigonometry and want to locate gaps before reviewing the course. It samples function notation, domains and ranges, graph reading, transformations, composition, inverses, multiplicative change and right-triangle ratios. Beginners can start with the foundations without taking this diagnostic.

Attempt the questions independently and note any unfamiliar notation. A calculator is unnecessary: the examples use exact values and simple arithmetic so that the results reflect conceptual readiness. Read plotted information from the supplied axes and distinguish input values from output values. Select-all items require checking each statement separately. Save the worked explanations for review after your initial attempt.

Use the results to choose targeted review within the functions, exponential functions and trigonometry modules. A correct choice reached by guessing is weaker evidence than a correct choice supported by a clear reason; a missed item can point to a useful starting lesson. This short sample has no pass/fail threshold and does not establish complete mastery of the later modules. Recheck repaired skills using unfamiliar examples.