ACT Preparation / Unit 10 ACT 0904 worked example, 60 to 90 seconds
Evaluating and Solving With Function Notation
The idea
Function-notation questions run in two directions, each with its method. To evaluate f(a), substitute a for every x and simplify, using parentheses. To solve f(x) = k, set the formula equal to k and solve for x; there may be more than one answer. From a table, find the input's row to evaluate, or the output's rows to solve. From a graph, go up from the input to evaluate, or across from the output to solve.
In practice
Worked example: f(x) = 2x² − 5. Evaluate f(−3): 2(−3)² − 5 = 18 − 5 = 13. Solve f(x) = 27: 2x² − 5 = 27, so x² = 16, and x = 4 or x = −4. Second, from a table: if g(2) = 9 and g(5) = 9, then solving g(x) = 9 gives x = 2 and x = 5.
Where people slip
Solving can return several inputs for one output, which is allowed; evaluating always returns exactly one output, because f is a function.
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