Practice and Problem-Solving Exercises

A Practice

Describe how each graph is related to the graph of y = | x | . bold italic y equals vertical line bold italic x vertical line .  See Problem 1.

Graph each function by translating y = | x | . bold italic y equals vertical line bold italic x vertical line .  See Problem 2.

9. y = | x | − 3 y equals vertical line x vertical line negative 3
10. y = | x | + 7 y equals vertical line x vertical line plus 7
11. y = | x | + 3 y equals vertical line x vertical line plus 3
12. y = | x | − 6 y equals vertical line x vertical line negative 6
13. y = | x | + 6 y equals vertical line x vertical line plus 6
14. y = | x | − 2.5 y equals vertical line x vertical line negative 2.5

Write an equation for each translation of y = | x | . bold italic y equals vertical line bold italic x vertical line .  See Problem 3.

15. 9 units up
16. 7 units down
17. 0.25 unit up
18. 3.25 units down
19. 5.9 units up
20. 1 unit down

Graph each function by translating y = | x | . bold italic y equals vertical line bold italic x vertical line .  See Problem 4.

21. y = | x − 3 | y equals vertical line x minus 3 vertical line
22. y = | x + 3 | y equals vertical line x plus 3 vertical line
23. y = | x − 1 | y equals vertical line x minus 1 vertical line
24. y = | x + 6 | y equals vertical line x plus 6 vertical line
25. y = | x − 7 | y equals vertical line x minus 7 vertical line
26. y = | x + 2.5 | y equals vertical line x plus 2.5 vertical line

Write an equation for each translation of y = | x | . bold italic y equals vertical line bold italic x vertical line .  See Problem 5.

27. left 9 units
28. right 9 units
29. right 0.5 unit
30. left 3 2 units 3 halves , units
31. left 5 2 units 5 halves , units
32. right 8.2 units

B Apply

Below graph of y = − | x | . bold italic y equals negative vertical line bold italic x vertical line .  Graph each function by translating y = − | x | . bold italic y equals negative vertical line bold italic x vertical line .

33. y = − | x | + 3 y equals negative vertical line x vertical line plus 3
34. y = − | x | − 3 y equals negative vertical line x vertical line negative 3
35. y = − | x + 3 | y equals negative vertical line x plus 3 vertical line
36. y = − | x − 3 | y equals negative vertical line x minus 3 vertical line

Write an equation for each translation of y = − | x | . bold italic y equals negative vertical line bold italic x vertical line .

37. 2 units up
38. 2.25 units left
39. 15 units down
40. 4 units right
41. Writing Explain how the relationship between y = | x | y equals vertical line x vertical line  and y = | x | + k y equals vertical line x vertical line plus k  is similar to the relationship between y = m x y equals m x  and y = m x + b . y equals m x plus b .
42. Reasoning Make a table of values for y = | x | y equals vertical line x vertical line  and y = | x | + 5 . y equals vertical line x vertical line plus 5 .  How do the y-values for corresponding x-values compare?

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