Evaluating f(3) and f(a+2)

Pre-Calculus · Axiom Academy

EXAMPLE Evaluating f(3) and f(a+2) Substitute a number, then a whole expression, into the same function — step by step. Given the function f(x) = 2x^2 - 3x + 1 , find both f(3) and f(a+2) . The variable x is just a placeholder — whatever goes inside the parentheses takes its place everywhere it appears. Nice work — you evaluated the same function at a number and at an expression, all by the same substitution rule. Substitution is replacement: wherever you see x , drop in the entire input — whether it's 3 or a+2 — and keep it in parentheses. Parentheses prevent mistakes: writing 2(a+2)^2 and -3(a+2) keeps the square and the sign attached to the whole input. The results: f(3) = 10 and f(a+2) = 2a^2 + 5a + 3 . That second answer is exactly the machinery behind the difference quotient in calculus — evaluating a function at an expression is a skill you'll lean on constantly.

This is the written version of the interactive lesson above. See the full Pre-Calculus course.