Section 3.6 – Absolute Value Functions

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:

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

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

Recall Solving Absolute Value Equations Solve algebraically and graphically.

Recall Solving Absolute Value Equations Solve algebraically and graphically.

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

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