Functions & Notation

Function notation is just a label for "the output of this rule at this input": $f(3)$ means substitute $3$ for $x$ and simplify — minding signs, exponents, and piecewise conditions. Transforming a graph follows tidy rules: shifting left by $k$ replaces $x$ with $x + k$, a constant outside shifts up or down, and a factor in front stretches or compresses. These are real, released Regents questions.