1. Lesson 2- Modulus Function 18 December, 2015ML2 MH Objectives : - What is the Modulus Function ? - Graphs of Modulus function - Solving inequalities involving modulus

2. What is it? “The modulus of x” “The absolute value of x” Basically means the distance from 0 ALWAYS POSITIVE 18 December, 2015ML2 MH

3. What is it? 18 December, 2015ML2 MH

4. What is it? Evaluate this: 18 December, 2015ML2 MH

5. What is it? Find the value of f(-3) in the following function: 18 December, 2015ML2 MH

6. Graphs x-3-20123 Now plot these values on a graph Copy and complete the following table: 18 December, 2015ML2 MH

7. Graphs 18 December, 2015ML2 MH

8. Graphs (2) x-4-3-201234 Now plot these values on a graph Copy and complete the following table: 18 December, 2015ML2 MH

9. Graphs (2) 18 December, 2015ML2 MH

10. Inequalities |f(x)| is the positive value of f(x) |x | = x if x > 0 and |-x | = x if x < 0 and so |-7|is 7 Conversely |x|=3 means x is 3 or -3 |x|≤3 means -3 ≤ x ≤ 3 18 December, 2015ML2 MH

11. Example 1. Solve 18 December, 2015ML2 MH Any other ways to solve this ??

12. Example 2. Solve OR could........

13. Example 3. Solve 18 December, 2015ML2 MH But x≥2 so this is inconsistent as can be seen from the graph Or

14. Important Note Note: The solutions to modulus questions need to be checked in the initial equation, as there may be an extra solution which is not consistent with the initial equation and is WRONG! This can also be shown by drawing a graph. ►Exercises C3/C4 page 59 Ex 3F 18 December, 2015ML2 MH