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Moduli functions

Department NameUniversity of Leicester

Content

Inverse functions

Modulus function

Inequalities with moduli

Introduction

Introduction

Modulus functions

Inequalities with moduli

Next

Introduction

Modulus

The modulus (or absolute) function is written as and produces the graph

Next

Modulus functions

Inequalities with moduli

Introduction

Modulus of other functions

𝑦=sin 𝑥

𝑦=|sin𝑥|

The modulus effectively reflects all the values below the horizontal axis in the line

Next

Modulus functions

Inequalities with moduli

Introduction

Plotting

Enter numbers between -10 and 10:y = | x + |

2 4 6 80

2

-2

-1

0

1

3

-3

-4

1 3 5 7-4 -2-5 -3 -1-6

Next

Modulus functions

Inequalities with moduli

Introduction

Plot without modulus sign

Plot with modulus sign

Clear

Plot without modulus sign

Plot with modulus sign

Question

2 4 6 80

2

4

6

0

1

3

5

1 3 5 7-4 -2-5 -3 -1-6

Select Answe

r

Select Answe

r

Select Answe

r

Which of these is the graph of ?

Select Answe

r

Modulus functions

Inequalities with moduli

Introduction

Question

20

2

4

6

0

1

3

5

1 3-4 -2-5 -3 -1-6

Which of these is the graph of ?

Select Answe

r

Select Answe

rSelect Answe

r

Select Answe

r

Modulus functions

Inequalities with moduli

Introduction

Question

Modulus functions

Inequalities with moduli

Introduction

Which of these is the graph of ?

Inequalities with moduli

2 4 6 80

2

-2

-1

0

1

3

-3

-4

1 3 5 7-4 -2-5 -3 -1-6

| x + | < | x + |(This line is in blue) (This line is in pink)

Next

Modulus functions

Inequalities with moduli

Introduction

Plot the 2 lines

Clear

Shade valid region

Question

2 4 6 80

2

4

0

1

3

5

1 3 5 7-4 -2-5 -3 -1-6

𝑦=¿ 𝑥+4∨+1

𝑥<−0.2

𝑥<0−4<𝑥<0

or

𝑥>3

𝑥>−0.2

−0.2<𝑥<3−0.2<𝑥<1

or

The graphs of and are shown. What is the solution to ?

6

𝑦=¿ 4 𝑥 – 4∨¿

Modulus functions

Inequalities with moduli

Introduction

Conclusion

Modulus functions

Inequalities with moduli

Next

Introduction

You should now be able to:

Recognise and draw the graphs of functions with moduli in them.

Solve inequalities with moduli in them.