SAT and ACT math terms · SAT Math, ACT Math
Function notation
Function notation: Writing f(x) to show the output of function f for input x.
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What it means
f(3) means substitute 3 for x in the function's rule. Composite functions apply one function to the output of another: f(g(x)). Transformations change a function's graph: f(x) + k shifts it up, f(x − h) shifts it right, and −f(x) reflects it over the x-axis.
Function notation lets questions describe relationships compactly, so reading it accurately is essential.
Example
If f(x) = 2x² − 1, then f(3) = 2(9) − 1 = 17, and f(x + 1) = 2(x + 1)² − 1.
On the exam
Both tests use function notation in algebra and modeling questions; the ACT tests composition and transformations directly.