6.4 absolute-value functions

6.4 Absolute-Value FunctionsObjectives: Explore features of the absolute-value

function. Explore basic transformations of the absolute-value function.

Standards Addressed: 2.8.11.O: Determine the domain and range of a relation. 2.8.11.Q: Represent functional relationship in tables, charts, and graphs.

The first coordinates in the set of ordered pairs are the domain of the relation, and the second coordinates are the range of

the relation.

Ex. 1

A.Domain All RealsRange y > 0

Ex. 2 Find the domain and range of each function. Then graph each function.

Domain All Reals Range y > 0

b. Y = I7xI

Domain all real numbers Range y > o

c. Y = Ix – 4I

Domain all real #s Range y > 4

D. Y = IxI -4

Types of Transformations:

Types of Transformations:

Ex. 3

Reflect x axis Vertical Translation down 4

C. Y = - IxI - 4

Horizontal Translation Right 10 Vertical Translation up 2

D. Y = Ix – 10I + 2

Horizontal Compression 1/6 Horizontal Translation Right

E. Y = I6x – 1I

Reflection x axis Vertical Stretch 3

F. Y = -3IxI

2. What happens to the graph of the function y = IxI when it is reflected through the y-axis verse the x-axis?

3. How does the graph of y = 3IxI compare with the graph of y = IxI?