1. Section 3.6 – Absolute Value Functions

2. Absolute Value Functions
The absolute value function can be defined as a piecewise function.
𝑓 𝑥 = 𝑥 = 𝑥 , 𝑥≥0 −𝑥, 𝑥<0
Domain: (−∞, ∞)
Range: [0, ∞)
Domain:
Range:

3. Graphing Absolute Value Functions
Graph the absolute value function by using transformations.
Basic Graph: 𝑓 𝑥 = 𝑥
Shift graph of 1 unit to the left
Shift graph 4 units down

4. Graphing Absolute Value Functions
Graph the absolute value function by using transformations.
Basic Graph: 𝑓 𝑥 = 𝑥
Shift graph of 3 unit to the right
Reflect over 𝑥−axis
Shift graph 4 units down

5. Recall Solving Absolute Value Equations
Solve algebraically and graphically.

6. Recall Solving Absolute Value Equations
Solve algebraically and graphically.

7. Solving Absolute Value Equations - Graphing
Solve algebraically and graphically using the software..

8. Solving Absolute Value Equations - Graphing
Solve algebraically and graphically.
Since the absolute value can’t be negative, there is no solution. { }