Lesson 7: Graphing Absolute Value Functions — Practice Questions

1. 1. The graph of the function $f(x) = |x - 5| + 2$ has a vertical axis of symmetry. What is the equation of this line? $x = \_\_\_$

2. 2. Which of the following is the axis of symmetry for the graph of the function $y = 3|x + 4| - 1$?

   • A. $x = 4$
   • B. $x = -4$
   • C. $y = 4$
   • D. $y = -4$

3. 3. The graph of an absolute value function has an axis of symmetry at $x = 1$. If $(5, 3)$ is a point on the graph, which of the following points must also be on the graph?

   • A. (-5, 3)
   • B. (-3, 3)
   • C. (1, 3)
   • D. (3, 5)

4. 4. What is the equation for the axis of symmetry of the function $g(x) = -5|x + 7| - 10$? The equation is $x = \_\_\_$.

5. 5. The vertex of the absolute value function $f(x) = |x - 9| + 4$ is located at the point $(9, \_\_\_)$.

6. 6. What are the coordinates of the vertex for the function $g(x) = 5|x + 2| - 3$?

   • A. (2, -3)
   • B. (-2, -3)
   • C. (2, 3)
   • D. (-2, 3)

7. 7. Find the vertex of the function $p(x) = |2x + 10| - 1$.

   • A. (-5, -1)
   • B. (5, -1)
   • C. (-10, -1)
   • D. (-5, 1)

8. 8. Which of the following functions has its vertex at the point $(1, -6)$?

   • A. f(x) = |x + 1| - 6
   • B. f(x) = |x - 1| + 6
   • C. f(x) = |x + 6| - 1
   • D. f(x) = |x - 1| - 6