Www.le.ac.uk Numerical Methods: Integration Department of Mathematics University of Leicester.
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Transcript of Www.le.ac.uk Moduli functions Department Name University of Leicester.
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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.