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Objectives : - What is the Modulus Function ? - Graphs of Modulus function - Solving inequalities involving modulus

What is it?

x“The modulus of x”

“The absolute value of x”

Basically means the distance from 0

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What is it?

44 22

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What is it?

57 Evaluate this:

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What is it?

24|5| xxf

Find the value of f(-3) in the following function:

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Graphs

xx -3-3 -2-2 -1-1 00 11 22 33

Now plot these values on a graph

Copy and complete the following table:

xy

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Graphs

-1

0

1

2

3

-3 -2 -1 0 1 2 3

xy

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Graphs (2)

xx -4-4 -3-3 -2-2 -1-1 00 11 22 33 44

Now plot these values on a graph

Copy and complete the following table:

42 xy

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-1

0

1

2

3

4

5

-3 -2 -1 0 1 2 3

Graphs (2)

42 xy

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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

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Example 1. Solve

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3|2| x

Any other ways to solve this ??

Example 2. Solve

OR could ........

|12||2| xx

Example 3. Solve

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12|2| xx

But x≥2 so this is inconsistent as can be seen from the graph

Or

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

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