Absolute Value Equations and Inequalities Test

Flashcard
•
Mathematics
•
9th - 12th Grade
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the definition of absolute value?
Back
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted as |x|.
2.
FLASHCARD QUESTION
Front
How do you solve the equation |x + 10| = 11?
Back
To solve |x + 10| = 11, set up two equations: x + 10 = 11 and x + 10 = -11. Solving these gives x = 1 and x = -21.
3.
FLASHCARD QUESTION
Front
What does the graph of y = |x| look like?
Back
The graph of y = |x| is a V-shaped graph that opens upwards, with the vertex at the origin (0,0).
4.
FLASHCARD QUESTION
Front
What is the solution set for the inequality |x| < 3?
Back
The solution set for |x| < 3 is -3 < x < 3.
5.
FLASHCARD QUESTION
Front
How do you interpret the inequality |x - 4| > 2?
Back
The inequality |x - 4| > 2 means that x is either less than 2 or greater than 6.
6.
FLASHCARD QUESTION
Front
What is the effect of a negative coefficient in front of an absolute value function, such as y = -|x|?
Back
A negative coefficient reflects the graph of the absolute value function across the x-axis.
7.
FLASHCARD QUESTION
Front
How do you graph the inequality |x + 2| ≤ 4?
Back
To graph |x + 2| ≤ 4, find the critical points by solving x + 2 = 4 and x + 2 = -4, which gives x = 2 and x = -6. Shade the region between -6 and 2, including the endpoints.
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