2.5E: Absolute Value Functions (Exercises)
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. \(| x-2 |\ge 3\)
24. \(| x+4 |\ge 2\)
25. \(| 3x+9 |<4\)
26. \(| 2x-9 |\le 8\)
- Answer
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1. \(y = \dfrac{1}{2}|x + 2| + 1\)
3. \(y = -3|x - 3| + 3\)
5.
7.
9.
11. \(x = -\dfrac{9}{5}\) or \(x = \dfrac{13}{5}\)
13. \(x = \dfrac{1}{2}\) or \(x = \dfrac{15}{2}\)
15. \(x = -\dfrac{5}{3}\) or \(x = -\dfrac{1}{3}\)
Horizontal Intercepts Vertical Intercept 17. (-6, 0) and (4, 0) (0, -8) 19. none (0, -7) 21. \(-11 < x < 1\) or (-11, 1)
23. \(x \ge 5\), \(x \le -1\) or \((-\infty, -1] \cup [5, \infty)\)
25. \(-\dfrac{13}{3} < x < -\dfrac{5}{3}\) or \((-\dfrac{13}{3}, -\dfrac{5}{3})\)