Absolute Value Equations, Functions, and Inequalities
Grade 9 Math worksheet covering absolute value equations, functions, and inequalities with various question types.
Includes
Standards
Topics
Absolute Value Equations, Functions, and Inequalities
Name:
Date:
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. Which of the following is the solution to the equation |x - 3| = 5?
x = 8
x = -2
x = 8 or x = -2
No solution
2. What is the range of the function f(x) = |x| + 2?
(-∞, ∞)
[0, ∞)
[2, ∞)
(-∞, 2]
3. The absolute value of a number is its distance from on the number line.
4. When solving an absolute value inequality like |x| < a, the solution will be a inequality.
5. Solve the inequality |2x - 1| ≥ 7 and graph the solution on a number line.
6. The graph of an absolute value function always forms a 'V' shape.
True
False
7. The equation |x| = -3 has two solutions.
True
False
8. A company produces widgets, and the ideal weight of a widget is 10 grams. The manufacturing process allows for a tolerance of 0.5 grams. Write an absolute value inequality that represents the acceptable range of weights for a widget, and then solve it.
9. Graph the function f(x) = |x + 1| - 3 on the coordinate plane below.
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