2.5E: Absolute Value Functions (Exercises)
( \newcommand{\kernel}{\mathrm{null}\,}\)
section 2.5 exercise
Write an equation for each transformation of f(x)=|x|
1. 2.
3. 4.
Sketch a graph of each function
5. f(x)=−|x−1|−1
6. f(x)=−|x+3|+4
7. f(x)=2|x+3|+1
8. f(x)=3|x−2|−3
9. f(x)=|2x−4|−3
10. f(x)=|3x+9|+2
Solve each the equation
11. |5x−2|=11
12. |4x+2|=15
13. 2|4−x|=7
14. 3|5−x|=5
15. 3|x+1|−4=−2
16. 5|x−4|−7=2
Find the horizontal and vertical intercepts of each function
17. f(x)=2|x+1|−10
18. f(x)=4|x−3|+4
19. f(x)=−3|x−2|−1
20. f(x)=−2|x+1|+6
Solve each inequality
21. |x+5|<6
22. |x−3|<7
23. |x−2|≥3
24. |x+4|≥2
25. |3x+9|<4
26. |2x−9|≤8
- Answer
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1. y=12|x+2|+1
3. y=−3|x−3|+3
5.
7.
9.
11. x=−95 or x=135
13. x=12 or x=152
15. x=−53 or x=−13
Horizontal Intercepts Vertical Intercept 17. (-6, 0) and (4, 0) (0, -8) 19. none (0, -7) 21. −11<x<1 or (-11, 1)
23. x≥5, x≤−1 or (−∞,−1]∪[5,∞)
25. −133<x<−53 or (−133,−53)