Functions — Input, Output, Notation

f(x) means "the output when you input x."

If f(x) = 2x + 3, then f(4) = 2(4) + 3 = 11.

Domain: All possible inputs (x-values). Look for division by zero and square roots of negatives — those create restrictions.

Range: All possible outputs (y-values).

Composition: f(g(x)) means plug g(x) into f.

If f(x) = x2 and g(x) = x + 1, then f(g(3)) = f(4) = 16.

Interpreting graphs:

f(2) = 5 means the point (2, 5) is on the graph

f(x) = 0 means the x-intercepts

f(0) = the y-intercept

SAT favorite: "For what value of x is f(x) = g(x)?" Find where the two graphs intersect.

Reference:

Wikipedia: Function

https://en.wikipedia.org/wiki/Function_(mathematics)