Absolute Value Equations, Functions, and Inequalities

Grade 9 Math worksheet covering absolute value equations, functions, and inequalities with various question types.

Grade 9 Math AlgebraAbsolute Value Equations Functions and Inequalities

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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseLong AnswerGraph

Standards

CCSS.MATH.CONTENT.HSA.CED.A.1CCSS.MATH.CONTENT.HSA.REI.B.3CCSS.MATH.CONTENT.HSF.IF.A.1

Topics

AlgebraAbsolute ValueEquationsInequalitiesFunctions

8 sections · Free to use · Printable

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Absolute Value Equations, Functions, and Inequalities

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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.