1. 2.7 – Use of Absolute Value Functions and Transformations

2. A transformation changes a graph’s size, shape, position, or orientation. A translation is a transformation that shifts a graph horizontally and/or vertically, but does not change its size, shape, or orientation.

3. 2.7 – Use of Absolute Value Functions and Transformations The graph of y = |x – h| + k is the graph of y = |x| translated h units horizontally and k units vertically. The vertex would be (h, k)

4. 2.7 – Use of Absolute Value Functions and Transformations

5. When a = -1, the graph of y = a|x| is a reflection in the x-axis of the graph of y = |x|. When a < 0, but a doesn’t equal -1, the graph of y = a|x| is a vertical stretch or shrink with a reflection in the x-axis of the graph of y = |x|.

6. 2.7 – Use of Absolute Value Functions and Transformations Example : Graph the function and compare the graph with the graph of y = |x|: y = |x -2| + 5 Y = ¼|x| f(x) = -3|x + 1| - 2

7. 2.7 – Use of Absolute Value Functions and Transformations Transformations of General Graphs

8. 2.7 – Use of Absolute Value Functions and Transformations Example: The graph of a function y = f(x) is shown. Sketch the graph of the given function. a. y = 2f(x) b.y = -f(x + 2) + 1 c.y =.5f(x) d.y = 2f(x – 3) – 1