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📚 Modeling, Functions, and Graphs
Chapters ▾
1 Functions and Their Graphs2 Modeling with Functions3 Power Functions4 Exponential Functions5 Logarithmic Functions6 Quadratic Functions7 Polynomial and Rational Functions8 Linear Systems9 Sequences and Series10 Algebra Skills Refresher11 Using a Graphing Calculator12 Using a GeoGebra Calculator App13 Glossary14 Properties of Numbers15 Geometry formulas16 GNU Free Documentation License

11.7 Function Notation and Transformation of Graphs

Function Notation

The calculator uses Y 1 ( X ) , Y 2 ( X ) , 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 = − 1 2 f ( x ) with that of y = f ( x ) .

Define Y 1 = X 2 and Y 2 = − 1 / 2 ∗ Y 1 ( X ) . Press to see the graphs (Figure).

GC vertical reflection of parabola

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.