Absolute Value
Solve |x − 5| = 9.
A. {14, −4}
B. {4, −14}
C. {14, 4}
D. {−14, −4}
What is {14, −4}?
Solve the system: y = x + 1 and 2x + y = 10.
A. (2, 3)
B. (3, 4)
C. (4, 5)
D. (3, 5)
What is (3,4)?
1. A plant grows 4 cm each week. At week 2 it is 13 cm tall. What height does the model predict at week 6?
A. 25 cm
B. 29 cm
C. 31 cm
D. 37 cm
What is 29cm?
13+4(4)=29
Solve: |x − 2| < 5.
A. −3 < x < 7
B. x < −3 or x > 7
C. −7 < x < 3
D. x > 7
What is −3 < x < 7?
For f(x) = |x|, which statement is true about (0, 0)?
A. It is the maximum only.
B. It is the minimum and both intercepts.
C. It is the y-intercept only.
D. It is not an intercept.
What is the minimum and both intercepts?
Solve: 4|x + 1| = 20.
A. {4, −6}
B. {6, −4}
C. {−4, 6}
D. {5, −5}
What is {4, −6}?
What is x?
2x + y = 14 A. 3
x − y = 1. B. 4
C. 5
D. 6
What is x=5?
A model is y = 1.5x + 2. If x = 8, what is y?
A. 10
B. 12
C. 14
D. 16
What is y = 1.5(8) + 2 = 14?
Which point satisfies both y ≥ x − 1 and y ≤ −x + 5?
A. (4, 0)
B. (1, 2)
C. (0, 6)
D. (3, 3)
What is (1,2)?
A V-shaped graph has vertex (0, 0) and passes through (2, 10). Which equation represents it?
A. f(x) = 5|x|
B. f(x) = |x| + 5
C. f(x) = 2|x| + 10
D. f(x) = |5 − x|
What is y=5|x|?
Solve: |3x − 6| = 15.
A. {−3, 7}
B. {3, −7}
C. {−7, 3}
D. {7, −3}
What is {7, −3}?
Solve the system:
x + y + z = 7 A. (2, 1, 4)
x − y + z = 5 B. (1, 2, 4)
2x + y − z = 1. C. (2, 4, 1)
D. (4, 1, 2)
What is (2, 1, 4)?
The data are (1, 7), (2, 10), (3, 13), (4, 16). Which equation models the data?
A. y = 3x + 4
B. y = 4x + 3
C. y = 3x + 7
D. y = 2x + 5
What is y=3x+4?
Product A uses 4 kg of material and 2 machine hours; product B uses 3 kg and 1 machine hour. At most 48 kg and 20 machine hours are available. Which system models the limits?
A. 4x + 3y ≤ 48; 2x + y ≤ 20
B. 3x + 4y ≤ 48; x + 2y ≤ 20
C. 4x + 3y ≥ 48; 2x + y ≥ 20
D. 4x + 2y ≤ 48; 3x + y ≤ 20
What is 4x + 3y ≤ 48; 2x + y ≤ 20?
At most- ≤
An absolute value graph opens upward, has vertex (−2, 4), and is vertically stretched by a factor of 3. Which equation is correct?
A. y = −3|x + 2| + 4
B. y = 3|x − 2| + 4
C. y = 3|x + 2| + 4
D. y = |x + 2| + 3
What is y = 3|x + 2| + 4?
Solve: 3|x − 2| + 1 < 1.
A. x < 2
B. x > 2
C. All real numbers
D. No solution
What is No solution?
Solve: 3x + y = 13 and x − y = 3.
A. (2, 7)
B. (4, 1)
C. (3, 4)
D. (5, −2)
What is (4,1)?
A math club has 86 students. There are 14 more ninth-graders than tenth-graders. Let n be ninth-graders and t be tenth-graders. Which system models the situation?
A. n + t = 86; n = t − 14
B. n − t = 86; n = t + 14
C. n + t = 14; n = t + 86
D. n + t = 86; n = t + 14
What is n + t = 86; n = t + 14?
For y ≥ 2x − 1 and y ≥ −x + 2, which region is shaded?
A. Below both dashed lines
B. Above both solid lines
C. Between the lines only
D. Below the first and above the second
What is above both solid lines?
A relation has domain [−6, 3] and range [−4, 9]. Which statement is correct?
A. x-values run from −4 to 9.
B. y-values run from −6 to 3.
C. Both domain and range are [−6, 9].
D. x-values run from −6 to 3 and y-values from −4 to 9.
What is x-values run from −6 to 3 and y-values from −4 to 9?
Solve: 12 − 2|x + 3| = 2.
A. {−2, −4}
B. {2, −8}
C. {−8, 2}
D. {−1, −5}
What is {2, −8}?
Solve the system: y = −x + 6 and y = x².
A. (−2, 4) and (3, 9)
B. (−3, 9) and (2, 4)
C. (−2, 4) and (3, 9)
D. (−2, 4) and (2, 4)
What is (−3, 9) and (2, 4)?
x=-3 or 2 and y=9 and 4
A robot's distance from its starting point is 3, 6, 9, 12, 15 when time is −1, −2, −3, −4, −5 (and the pattern is symmetric for positive time). Which function models the distance?
A. d(t) = |t| + 3
B. d(t) = 3|t|
C. d(t) = |3t| + 1
D. d(t) = 3|t| + 1
What is d(t) = 3|t|?
A graph includes every point from x = −5 to x = 7 and from y = −2 to y = 4, including all endpoints. What are the domain and range?
A. Domain (−5, 7), Range (−2, 4)
B. Domain [−2, 4], Range [−5, 7]
C. Domain [−5, 7], Range [−2, 4]
D. Domain [−5, 4], Range [−2, 7]
What is Domain [−5, 7], Range [−2, 4]?
Find the domain, range, and minimum of g(x) = 4|x − 3| − 2.
A. Domain x ≥ 3; range y ≥ −2; minimum −2
B. Domain all real numbers; range y ≥ −2; minimum −2 at x = 3
C. Domain all real numbers; range y ≤ −2; maximum −2
D. Domain all real numbers; range y ≥ 3; minimum 3
What is Domain all real numbers; range y ≥ −2; minimum −2 at x = 3?