Evaluating a Function — Cheat sheet

Key method

For $f(x)=x^2-3x$, input $u$ gives $f(u)=u^2-3u$. If $u$ is an expression, expand only after substitution. Check domain restrictions first.

Example

Compute $f(a+h)$:

Subtracting $f(a)$ leaves $2ah+h^2-3h$. If $h\ne0$, dividing by $h$ gives $2a+h-3$, the difference quotient used in differentiation.

Avoid this mistake

$f(a+h)$ is usually not $f(a)+f(h)$. A nonlinear function does not distribute over addition.