3. The Modulus Function Objectives: Understand what an absolute value is. Solve equations and inequalities involving modulus. Graph modulus functions.

4. The Modulus Function SUMMARY To solve inequalities involving one or more modulus functions:  Sketch the functions. ( Type “abs” if a graphical calculator is used. )  Find the points of intersection using the related functions ( without the mod. signs ). ( A negative sign is needed for reflected parts. )  Refer to the graph to write the inequality for x.  Mark the section(s) of the x -axis that give the solution. Method 1:

5. The Modulus Function SUMMARY Method 2:  Square both sides of the inequality to remove the mod. signs and solve the resulting linear or quadratic inequality. ( A graph is needed for quadratic inequalities. )

6. The Modulus Function 1. x y Exercise Solutions: Solve the inequalities. 1.2.

7. The Modulus Function 1. x y Exercise Solutions: Solve the inequalities. 1.2. By symmetry, Or:

8. The Modulus Function A xx B x y Solutions: 2. For B: By symmetry, at A: So, ( One region so one inequality ) (N.B. Strict inequality )

9. The Modulus Function Method 2: Zeros: So:

10. The Modulus Function Activity Card match pair up the cards to solve the inequalities

11. The Modulus Function A x x B x y Exercise Solution: 1. Solve the inequalities. 1.2. For B, 3 For A, or So,

12. The Modulus Function Method 2: So, Zeros:

13. The Modulus Function A B x x Exercise 2. Solution: For B, For A, or: So, ( Two regions so two inequalities )

14. The Modulus Function Zeros: Method 2: So,

15. The Modulus Function