11.7 Function Notation and Transformation of Graphs

Function Notation

The calculator uses $Y sub 1 open parenthesis X close parenthesis$ , $Y sub 2 open parenthesis X close parenthesis$ , and so on, instead of $f (x)$ , $g (x)$ , and so on, for function notation.

Transformation of Graphs

We can use function notation to facilitate graphing transformations. In the examples below, we use $f (x) = x^{2}$ .

Translations

Vertical Scalings and Reflections

Compare the graph of $y = \frac{- 1}{2} f (x)$ with that of $y = f (x)$ .

Define $Y sub 1 equals X squared$ and $Y_{2} = - 1 / 2 * Y_{1} (X)$ . Press to see the graphs (Figure).

Modeling, Functions, and Graphs by Katherine Yoshiwara (yoshiwarabooks.org), GNU Free Documentation License 1.2 or later. Adapted for the XYZ HTML edition with the authors' permission (recorded 2026-07-04). License: GFDL-1.2-or-later.