1. Function Transformations

3. Definitions: Transformation – Operations that alter the form of a function. The common transformations are: translation (slide), reflection (or flip), compression (squeeze), dilation (stretch). Translation (slide) – a “sliding” of the graph to another location without altering its size or orientation. Reflection (flip) – the creation of the mirror image of a function across a line called the axis of reflection. Horizontal Compression (squeeze) – the squeezing of the graph towards the y-axis. Vertical Compression – the squeezing of the graph towards the x-axis. Horizontal Dilation (stretch) – the stretching of the graph away from the y-axis. Vertical Dilation – the stretching of the graph away from the x-axis.

4. Meaning of the notation: a · f(x) – multiply “f(x)” by “a” (multiply the “y-value” by “a”) f(|x|) – wherever the “x-value” is negative, make it positive. f(x) + d – add “d” to “f(x)” (add “d” to the “y-value”) f(x – c) – subtract “c” from the “x-value” and calculate f f(b·x) – multiply the “x-value” and “b” and calculate f. |f(x)| – wherever the function is negative, make it positive. (Wherever y is negative, make it positive).

5. Translations • • • • • 2 0 -6 4 -4 0 -2 6 0 4 • • • • •

6. Translations • • • • • 2 0 -2 4 0 0 2 6 4 8 • • • • •

7. Translations • • • • • 6 4 2 8 4 4 0 10 6 0 • • • • •

8. Translations • • • • • -4 -6 2 -2 4 -6 0 0 6 0 • • • • •

9. Reflections • • • • • 6 10 4 0 2 4 0 2 -2 -4 • • • • •

11. Reflections • • • • • -10 - 6 10 - 2 2 - 4 4 0 0 6 • • • • •

13. Compressions • • • • 0 4 -8 -2 -4 -6 0 2 2 6 • • • • • •

14. Dilations • • • • 0 8 0 -4 -2 4 2 -8 -4 4 • • • • • •

16. Absolute Value