Practice and Problem-Solving Exercises

A Practice

Make a table of values for each equation. Then graph the equation. See Problems 1 and 2.

8. y = | x | + 1 y equals vertical line x vertical line plus 1
9. y = | x | − 1 y equals vertical line x vertical line negative 1
10. y = | x | − 3 y equals vertical line x vertical line negative 3
11. y = | x + 2 | y equals vertical line x plus 2 vertical line
12. y = | x + 4 | y equals vertical line x plus 4 vertical line
13. y = | x + 5 | y equals vertical line x plus 5 vertical line
14. y = | x − 1 | + 3 y equals vertical line x minus 1 vertical line plus 3
15. y = | x + 6 | − 1 y equals vertical line x plus 6 vertical line negative 1
16. y = | x − 5 | + 4 y equals vertical line x minus 5 vertical line plus 4

Graph each equation. Then describe the transformation from the parent function f(x) = | x |. See Problem 3.

17. y = 3 | x | y equals 3 vertical line x vertical line
18. y = − 1 2 | x | y equals negative , 1 half , vertical line x vertical line
19. y = − 2 | x | y equals negative 2 vertical line x vertical line
20. y = 1 3 | x | y equals , 1 third , vertical line x vertical line
21. y = 3 2 | x | y equals , 3 halves , vertical line x vertical line
22. y = − 3 4 | x | y equals negative , 3 fourths , vertical line x vertical line

Without graphing, identify the vertex, axis of symmetry, and transformations from the parent function f(x) = | x |. See Problem 4.

23. y = | x + 2 | − 4 y equals vertical line x plus 2 vertical line negative 4
24. y = 3 2 | x − 6 | y equals , 3 halves , vertical line x minus 6 vertical line
25. y = 3 | x + 6 | y equals 3 vertical line x plus 6 vertical line
26. y = 4 − | x + 2 | y equals 4 minus vertical line x plus 2 vertical line
27. y = − | x − 5 | y equals negative vertical line x minus 5 vertical line
28. y = | x − 2 | − 6 y equals vertical line x minus 2 vertical line negative 6

Write an absolute value equation for each graph. See Problem 5.

Table of Contents