Absolute Value Equations, Functions, and Inequalities
A Grade 11 math worksheet covering absolute value equations, functions, and inequalities with various question types.
Includes
Standards
Topics
Absolute Value Equations, Functions, and Inequalities
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Read each question carefully and provide the best answer. Show all your work for full credit.
1. Solve for x: |2x - 3| = 7
2. Find the solutions to the equation: |x/3 + 2| - 1 = 4
3. Which of the following graphs represents the function f(x) = |x - 2| + 1?
A V-shape opening upwards with vertex at (2, 1)
A V-shape opening upwards with vertex at (-2, 1)
A V-shape opening downwards with vertex at (2, 1)
A V-shape opening downwards with vertex at (-2, 1)
4. Graph the function g(x) = -|x + 1| + 3. Clearly label the vertex and at least two other points.
5. Solve the inequality: |3x + 6| < 9
6. Solve and graph the solution set on a number line: |-2x + 4| ≥ 6
7. The absolute value of a number represents its from zero on a number line.
8. When solving an absolute value inequality of the form |ax + b| < c, the solution is typically written as a inequality.
9. The equation |x| = -5 has no real solutions.
True
False
10. The graph of an absolute value function always has a vertex.
True
False
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