Absolute Value Equations, Functions, and Inequalities
This worksheet covers solving and graphing absolute value equations, functions, and inequalities.
Includes
Standards
Topics
Absolute Value Equations, Functions, and Inequalities
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Read each question carefully and follow the instructions. Show all your work for full credit.
Solve each absolute value equation.
1. |x - 5| = 12
2. |2x + 3| - 4 = 9
Fill in the blanks regarding absolute value functions.
3. The graph of an absolute value function is V-shaped and symmetric about its .
4. The vertex of the function f(x) = |x - h| + k is at the point ( , ).
5. Which inequality represents all numbers x such that x is at most 7 units from 0?
|x| > 7
|x| < 7
|x| ≤ 7
|x| ≥ 7
Solve each absolute value inequality and graph the solution on a number line.
6. |x + 3| < 5
7. |2x - 1| ≥ 7
8. Graph the function f(x) = |x - 2| + 1 on the coordinate plane below.
Determine if the following statements are true or false.
9. The solution to |x| = -3 is x = 3 or x = -3.
True
False
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