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Transcript of Www.le.ac.uk Moduli functions Department Name University of Leicester.
![Page 1: Www.le.ac.uk Moduli functions Department Name University of Leicester.](https://reader030.fdocuments.in/reader030/viewer/2022032516/56649c575503460f948fdb66/html5/thumbnails/1.jpg)
www.le.ac.uk
Moduli functions
Department NameUniversity of Leicester
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Content
Inverse functions
Modulus function
Inequalities with moduli
Introduction
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Introduction
Modulus functions
Inequalities with moduli
Next
Introduction
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Modulus
The modulus (or absolute) function is written as and produces the graph
Next
Modulus functions
Inequalities with moduli
Introduction
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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
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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
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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
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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
![Page 9: Www.le.ac.uk Moduli functions Department Name University of Leicester.](https://reader030.fdocuments.in/reader030/viewer/2022032516/56649c575503460f948fdb66/html5/thumbnails/9.jpg)
Question
Modulus functions
Inequalities with moduli
Introduction
Which of these is the graph of ?
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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
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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
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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.
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