Absolute Value Equations, Functions, and Inequalities

Absolute Value Equations, Functions, and Inequalities

Read each question carefully and solve for the unknown. Show all your work for full credit.

1. Solve the following absolute value equation for x:

$$|2x - 5| = 11$$

2. Find the solutions for the equation:

$$|3x + 1| - 4 = 7$$

3. Graph the absolute value function $$f(x) = |x - 3| + 2$$. Identify the vertex and axis of symmetry.

Vertex:  

Axis of Symmetry:  

4. Solve the absolute value inequality and express your answer in interval notation:

$$|x + 4| < 7$$

5. Solve the inequality and graph the solution on a number line:

$$|2x - 1| \ge 5$$

6. Which of the following graphs represents the function $$y = -|x + 1| + 3$$?

7. The graph of an absolute value function is always  -shaped.

8. When solving an absolute value inequality of the form $$|ax + b| > c$$, it typically results in a   solution.

9. The vertex of the function $$f(x) = |x - h| + k$$ is at $$(h, k)$$.

10. An absolute value equation can never have more than two solutions.