2.7 – Use of Absolute Value Functions and Transformations

2.7 – Use of Absolute Value Functions and Transformations

• 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.

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)

2.7 – Use of Absolute Value Functions and Transformations

2.7 – Use of Absolute Value Functions and TransformationsWhen 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|.

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

2.7 – Use of Absolute Value Functions and TransformationsTransformations of General Graphs

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) + 1c. y = .5f(x)d. y = 2f(x – 3) – 1