Evaluating functions and solving for inputs

Evaluating functions and solving for inputs

Practise the two directions of function notation: calculating an output from a supplied input and finding inputs that produce a specified output. This precalculus set develops accurate substitution through rational, polynomial, absolute-value and square-root rules, then applies the same ideas to tables and simple contextual models.

Algebraic arguments require substituting the entire expression with careful parentheses. Questions also examine unavailable table entries, undefined evaluations, multiple inputs with a shared output and a parameter determined by a known function value. The bank progresses from direct evaluation to linked reasoning and error analysis without introducing difference quotients or derivatives.

Before you start

Review function notation, the distributive property and elementary equation solving. Use exact arithmetic, retaining fractions when appropriate. Identify whether the question gives an input or an output before beginning a calculation.

Practice and feedback

Attempt each calculation on paper before inspecting the choices. Single-select and select-all tasks include worked explanations and checks in the original rule. When an input is rejected, distinguish an algebraic failure from information that simply was not supplied. Explaining that distinction is as useful as obtaining a numerical result.