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

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 \((-\dfrac{13}{3}, -\dfrac{5}{3})\)