Topic 2
TEKS Cumulative Practice
Multiple Choice
Read each question. Then write the letter of the correct
answer on your paper.
1. Which inequality has a solution that matches the
graph below?
⫺4
⫺2
0
2
4
A. 0 x - 2 0 - 3 7 -2
6. Which of the following absolute value inequalities has
no solutions in Quadrant IV?
F. y + 2 Ú 0 x - 3 0
G. y 7 3 - 0 5 - x 0
H. y - 1 7 0 2x + 6 0
J. y … 0 4x 0 - 7
7. For which value of b would the equation
3 0 x - 2 0 = bx - 6 have infinitely many solutions?
B. 0 x - 2 0 6 -5
C. 0 x + 2 0 + 3 6 2
A. -6
C. -3
D. 0 x + 4 0 + 2 7 1
B. 3
D. 6
2. You used an oven thermometer while baking and found
out that the oven temperature varied between +7
degrees and -7 degrees from the setting. If your oven is
set to 325°F, let t be the actual temperature. What is the
absolute value inequality that represents this situation?
F. 0 t - 325 0 Ú 7
F. 69 … 0 t 0 … 91
G. 0 t - 325 0 6 7
G. 0 t - 80 0 … 11
H. 0 t - 7 0 … 325
H. 0 t - 69 0 … 91
J. 0 t - 325 0 … 7
3. A designer is designing a handbag. The height of
the handbag must be between 16 in. and 18 in.
The desirable height is 17 in. Which absolute value
inequality represents the height of the handbag?
A. 0 h - 16 0 … 1
C. 0 h - 17 0 Ú 2
B. 0 h - 17 0 … 1
D. 0 h - 18 0 Ú 2
4. How many negative solutions does 2 0 3x - 6 0 … 6
have?
F. 0
G. 1
8. A meteorologist predicts the daily high and low
temperatures as 91°F and 69°F. If t represents the
temperature, then this situation can be described with
the inequality 69 … t … 91. Which of the following
absolute value inequalities is an equivalent way of
expressing this?
H. 2
J. 0 t - 11 0 … 80
9. Which inequality has a solution that matches the
graph below?
⫺8 ⫺6 ⫺4 ⫺2
0
2
4
6
8
A. 0 x - 2 0 - 3 Ú 2
B. 0 x - 2 0 - 3 … 2
C. 0 x - 3 0 + 2 Ú 7
D. 0 x - 3 0 + 2 … 7
J. infinitely many
5. For which value of a does 4 = a + 0 x - 4 0 have no
solution?
A. -6
C. 4
B. 0
D. 6
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10. Which inequality best describes the graph?
2
⫺4
⫺2
15. Which equation is graphed?
y
O
4
x
⫺2
O
⫺4
x
2
4
⫺2
1
F. y … 2 0 x + 1 0 - 1
G. y Ú 12 0 x - 1 0 - 1
A. y = -3 0 x + 1 0 + 3
1
H. y … 2 0 x - 1 0 - 1
J. y Ú 12 0 x + 1 0 - 1
B. y = 3 0 x + 1 0 + 3
C. y = -3 0 x - 1 0 + 3
11. Which describes the translation of y = 0 x - 3 0 + 5?
A. y = 0 x 0 translated 3 units left and 5 units up
B. y = 0 x 0 translated 3 units right and 5 units up
D. y = 3 0 x + 1 0 - 3
16. How many x-intercepts does the graph of
y = 4 0 x - 12 0 - 9 have?
C. y = 0 x 0 translated 5 units left and 3 units up
F. 0
H. 2
D. y = 0 x 0 translated 5 units right and 3 units up
G. 1
J. 3
12. Which of the following ordered pairs is a solution
to the inequality y 7 13 0 x - 4 0 + 2?
F. (5, -1)
H. ( -1, 3)
G. (1, 3)
J. (2, 4)
13. Which of the following is not an important attribute of
absolute value functions?
A. Vertex
C. Rate of change
D. y-intercept
14. The graph of which equation is the graph of
f (x) = 0 x 0 reflected in the x-axis, translated 8 units left,
vertically compressed by a factor of 12 , and translated
down 5 units?
F. y = -2 0 x - 8 0 - 5
G. y = - 12 0 x - 8 0 - 5
H. y = 2 0 x + 8 0 - 5
J. y = - 12 0 x + 8 0 - 5
Topic 2
17. What is the y-intercept of y = 5 0 x - 2 0 - 7?
A. 2
C. 7
B. 3
D. -2
18. What is the axis of symmetry of y = 41 0 x + 6 0 - 3?
F. x = -3
G. y = -3
H. x = 6
B. Axis of symmetry
66
y
TEKS Cumulative Practice
J. x = -6
19. What is the equation of an absolute value function
with vertical stretch factor 31 and vertex (-3, 2)?
A. y = 31 0 x + 3 0 + 2
B. y = 31 0 x - 3 0 + 2
C. y = 3 0 x - 3 0 + 2
D. y = 31 0 x + 3 0 - 2
Gridded Response
20. What is the sum of the solutions of
0 2x + 4 0 - 6 = 8?
21. What is the greatest integer solution of
0 -2x - 5 0 - 3 … 2?
22. What is the sum of the solutions of
3 0 y - 4 0 = 9 and 0 y - 4 0 = 3?
23. What is the minimum of f (x) = 2 0 x + 1 0 - 3?
24. What is the horizontal translation of
f (x) = 3 0 x - 5 0 + 7?
25. What is the vertical stretch or compression factor of
f (x) = 12 0 x + 2 0 - 1?
26. What is the x-coordinate of the vertex of
f (x) = 0 x + 9 0 + 5?
27. If the point (a, 6) is an integer solution to
y 6 - 0 x - 3 0 + 7, what is the value of a?
Constructed Response
28. A new 10-lb dumbbell will pass inspection if it is
between 9.95 lb and 10.05 lb. What is the tolerance
of the weight of the dumbbell? What absolute value
inequality describes acceptable weights of the
dumbbell within an indicated tolerance? Show
all work.
Solve each equation or inequality. Graph the solution.
29. 4 - x = 0 2 - 3x 0
Graph each inequality.
35. y Ú x + 7
36. y 7 2 0 x + 3 0 - 3
37. 4x - 3y 6 2
38. y … - 12 0 x + 2 0 - 3
39. Graph y 6 0 x + 3 0 . Identify the parent function of the
boundary and describe the translation.
40. Solve the inequality y … 2 0 x - 3 0 - 4 algebraically.
41. Graphs of absolute value functions consist of portions
of two lines. What are the equations of the two lines
that appear in the graph of y = 2 0 x + 1 0 - 1? For
what values of x does each appear?
42. a. Write an absolute value equation that has exactly
two solutions.
b. Write an absolute value equation that has exactly
one solution.
c. Write an absolute value equation that has no
solutions.
d. How can you tell when an absolute value equation
of the form 0 x 0 = a will have exactly two solutions?
Exactly one solution? No solutions?
43. The absolute value of a real number is always
nonnegative. Is the output of an absolute value
function always nonnegative? Why or why not?
Justify your answer with an example.
44. Describe the transformations of y = -7 0 x + 41 0 - 13
from the parent function f (x) = 0 x 0 .
30. 5 0 3w + 2 0 - 3 7 7
Describe each transformation of the parent function
y = ∣ x ∣ . Then, graph each function.
31. y = 0 x 0 - 4
32. y = 0 x - 1 0 - 5
33. y = - 0 x + 4 0 + 3
34. y = 2 0 x + 1 0
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