Section 4.4: Absolute Value Graphically
Learning Objectives
In this section, you will:
- Graph linear absolute value functions.
- Graph quadratic absolute value functions.
Let’s Get Started…
You Tube’s the “All Around Math Guy” does a nice job of breaking up this process into two pieces. Check out Part 1: The Absolute Value of a Linear Function
Then, take things up a degree with the “All Around Math Guy’s” Part 2: The Absolute Value of a Quadratic Function
You can subscribe to The All Around Math Guy’s channel and/or see more helpful videos at: https://www.youtube.com/@AllAroundMathGuy
Section 4.4 Exercises
1. Check out Khan Academy’s Motion Problems with Definite Integrals.
- Practice problems follow the discussion.
- Answers are automatically checked!
This content comes directly from AndyMath.com’s Integrals of Absolute Value Functions
Access this resource for free at https://andymath.com/integrals-of-absolute-value-functions/
[Answers to odd problem numbers are provided at the end of the problem set. Just scroll down!]
1. [latex]\int_{0}^{3} |x-2| \,dx[/latex]
2. [latex]\int_{0}^{6} |2x-4| \,dx[/latex]
3. [latex]\int_{0}^{4} |x+3| \,dx[/latex]
4. [latex]\int_{0}^{4} |3x-6| \,dx[/latex]
5. [latex]\int_{-4}^{4} |x| \,dx[/latex]
6. [latex]\int_{0}^{3} |x+1| \,dx[/latex]
7. [latex]\int_{-1}^{4} |3x-5| \,dx[/latex]
8. [latex]\int_{-1}^{2} |5-x| \,dx[/latex]
9. [latex]\int_{-7}^{-3} -|x+5| \,dx[/latex]
Answers to Section 4.4 Odd Problems
1. 2.5
3. 20
5. 16
7. [latex]\frac{113}{6}[/latex]
9. -4
