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2.5.5E: 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 $$(-\dfrac{13}{3}, -\dfrac{5}{3})$$