Graphing Absolute Value Without a Calculator

Objective: You should be able to graph absolute value functions (including their changes) without a calculator.

Ex. Graph y x

Domain:

Range:

• A function that you should automatically know how to graph without plugging it into your calculator.

• Domain: All Reals

• Range: y > 0

y x

Translations to

Ex. Graph

Domain:Range: How do D and R change?

3 2y x

y x

Reflections to

Ex. Graph

Domain:Range: How do D and R change?

y x

y x

Stretching and Shrinking

Ex. Graph

Domain:Range: How do D and R change?

1

2y x

y x

Multiple Changes to

Ex. Graph

Domain:Range:

How do D and R change?

2y x

y x

Multiple Changes to

Ex. Graph

Domain:Range:

How do D and R change?

2 2 1y x

y x

Ex. Write the equation of the graph given.