Lesson 2 Modulus Function Objectives What is the

Lesson 2 - Modulus Function Objectives : - What is the Modulus Function ? - Graphs of Modulus function - Solving inequalities involving modulus * ML 2 MH

What is it? “The modulus of x” “The absolute value of x” Basically means the distance from 0 ALWAYS POSITIVE * ML 2 MH

What is it? * ML 2 MH

What is it? Evaluate this: * ML 2 MH

What is it? Find the value of f(-3) in the following function: * ML 2 MH

Graphs Copy and complete the following table: x -3 -2 -1 0 1 2 3 Now plot these values on a graph * ML 2 MH

Graphs * ML 2 MH

Graphs (2) Copy and complete the following table: x -4 -3 -2 -1 0 1 2 3 4 Now plot these values on a graph * ML 2 MH

Graphs (2) * ML 2 MH

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 * ML 2 MH

Example 1. Solve Any other ways to solve this ? ? * ML 2 MH

Example 2. Solve OR could. . . .

Example 3. Solve But x≥ 2 so this is inconsistent as can be seen from the graph Or * ML 2 MH

Important 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 C 3/C 4 page 59 Ex 3 F * ML 2 MH