Define functions precisely and use f(x) notation fluently.
A function is a rule that assigns exactly one output to each input. The domain is the set of all valid inputs; the range is the set of all possible outputs. We write f(x) to denote "the function f evaluated at x."
Vertical Line Test: a graph represents a function if and only if every vertical line crosses the graph at most once.
For rational functions, exclude values that make the denominator zero from the domain. For even-index radical functions, the radicand must be non-negative.
If f(x) = x² + 2x, find f(a + h). Substitute: f(a+h) = (a+h)² + 2(a+h) = a² + 2ah + h² + 2a + 2h.
Remember This!
When evaluating f(expression), replace every x with the entire expression — including using parentheses — before simplifying.
If f(x) = 2x − 5, what is f(−3)?