Graphing Absolute Value Equations PDF

Graphing Absolute Value Equations Part 1 1. What is the shape of the graph of an absolute value function? A) Parabola B) V-shape C) Line D) Circle Correct Answer: B) V-shape 2. What is the vertex of the absolute value function f(x) = |x|? A) (1, 0) B) (0, 1)...

Graphing Absolute Value Equations Part 1 1. What is the shape of the graph of an absolute value function? A) Parabola B) V-shape C) Line D) Circle Correct Answer: B) V-shape 2. What is the vertex of the absolute value function f(x) = |x|? A) (1, 0) B) (0, 1) C) (0, 0) D) (-1, 0) Correct Answer: C) (0, 0) 3. Which of the following is the graph of f(x) = |x - 3|? A) V-shape shifted 3 units right B) V-shape shifted 3 units left C) V-shape shifted 3 units up D) V-shape shifted 3 units down Correct Answer: A) V-shape shifted 3 units right Graphing Absolute Value Equations Part 2 4. What does the graph of f(x) = -|x| look like? A) V-shape pointing upwards B) V-shape pointing downwards C) U-shape pointing upwards D) Line Correct Answer: B) V-shape pointing downwards 5. In f(x) = a|x|, if a > 1, the graph will be: A) Stretched vertically B) Compressed vertically C) Shifted to the left D) Shifted to the right Correct Answer: A) Stretched vertically 6. What is the effect of a negative coefficient in front of the absolute value function, f(x) = -|x|? A) The graph opens up B) The graph opens down C) The graph shifts left  D) The graph shifts right Correct Answer: B) The graph opens down OC 6.2 Translating the Graph of f(x) = x 7. What is the effect of adding a constant to f(x) = |x|? A) Vertical stretch B) Vertical shift C) Horizontal shift D) Reflection Correct Answer: B) Vertical shift 8. What happens to the graph of f(x) = |x| if you subtract 2 from x (f(x) = |x - 2|)? A) The graph shifts 2 units left B) The graph shifts 2 units right C) The graph shifts 2 units up D) The graph shifts 2 units down Correct Answer: B) The graph shifts 2 units right 9. In f(x) = |x| + 4, what does the "+4" represent? A) Shift 4 units up B) Shift 4 units down C) Stretch by 4 D) Reflect over the x-axis Correct Answer: A) Shift 4 units up OC 6.3 Stretching, Shrinking, and Reflecting the Graph of f(x) = |x| 10. What is the effect of multiplying the absolute value function by a constant greater than 1? A) Vertical stretch B) Vertical shrink C) Horizontal stretch D) Reflection Correct Answer: A) Vertical stretch 11. What does multiplying the absolute value function by a fraction between 0 and 1 do? A) Vertical stretch B) Vertical shrink C) Horizontal shrink D) Horizontal shift Correct Answer: B) Vertical shrink  12. What happens when f(x) = -|x| compared to f(x) = |x|? A) Graph is shifted up B) Graph is reflected over the x-axis C) Graph is stretched D) Graph is compressed Correct Answer: B) Graph is reflected over the x-axis 13. Which of the following represents a vertical shrink of f(x) = |x|? A) f(x) = 2|x| B) f(x) = 0.5|x| C) f(x) = -|x| D) f(x) = |x + 2| Correct Answer: B) f(x) = 0.5|x| OC 6.4 Combining Transformations of the Graph of f(x) = |x| 14. Which equation represents a reflection over the x-axis and a vertical stretch of f(x) = |x|? A) f(x) = -2|x| B) f(x) = 2|x| C) f(x) = -|x + 2| D) f(x) = |x| - 2 Correct Answer: A) f(x) = -2|x| 15. What happens in the graph of f(x) = |x - 3| + 5? A) Shift 3 units left, 5 units down B) Shift 3 units right, 5 units up C) Shift 3 units right, 5 units down D) Shift 3 units left, 5 units up Correct Answer: B) Shift 3 units right, 5 units up 16. How does the graph of f(x) = |x + 1| - 2 compare to f(x) = |x|? A) Shift 1 unit left, 2 units down B) Shift 1 unit right, 2 units up C) Shift 1 unit left, 2 units up D) Shift 1 unit right, 2 units down Correct Answer: A) Shift 1 unit left, 2 units down 6.5 Solving Absolute Value Equations 17. What are the solutions to the equation |x| = 4? A) x = 4 B) x = -4 C) x = 4 or x = -4  D) x = 0 Correct Answer: C) x = 4 or x = -4 18. What is the first step to solve |x - 3| = 7? A) Add 3 to both sides B) Subtract 3 from both sides C) Set up two equations: x - 3 = 7 and x - 3 = -7 D) Set up two equations: x + 3 = 7 and x + 3 = -7 Correct Answer: C) Set up two equations: x - 3 = 7 and x - 3 = -7 19. Solve |x + 2| = 5. A) x = 3 B) x = 7 or x = -7 C) x = 3 or x = -7 D) x = 3 or x = -3 Correct Answer: D) x = 3 or x = -7 20. What are the solutions to the equation |x - 1| = 8? A) x = 1 B) x = 1 or x = -1 C) x = 9 or x = -7 D) x = 7 or x = -9 Correct Answer: C) x = 9 or x = -7 21. Solve |2x + 4| = 10. A) x = 3 or x = -7 B) x = 5 or x = -5 C) x = 2 or x = -2 D) x = 7 or x = -7 Correct Answer: A) x = 3 or x = -7 22. Solve |x| + 3 = 7. A) x = 7 or x = -7 B) x = 4 or x = -4 C) x = 3 or x = -3 D) x = 2 or x = -2 Correct Answer: B) x = 4 or x = -4 23. Which of the following equations has no solution? A) |x| = -5 B) |x| = 0 C) |x| = 1 D) |x| = 5 Correct Answer: A) |x| = -5 24. Solve |3x - 6| = 12. A) x = 6 or x = -6 B) x = 2 or x = -2 C) x = 3 or x = -3 D) x = 6 or x = 0 Correct Answer: D) x = 6 or x = 0  25. Solve |4x + 8| = 0. A) x = 2 B) x = -2 C) x = 0 D) No solution Correct Answer: B) x = -2 Challenge Questions 26. Which of the following represents a reflection and a shift of 2 units left? A) f(x) = -|x - 2| B) f(x) = -|x + 2| C) f(x) = |x - 2| + 2 D) f(x) = |x + 2| - 2 Correct Answer: B) f(x) = -|x + 2| 27. Solve |5x - 7| = 2. A) x = 1 or x = -1 B) x = 9/5 or x = 1 C) x = 5/9 or x = -5 D) x = 9/5 or x = 1 Correct Answer: B) x = 9/5 or x = 1 28. What transformation has occurred in f(x) = 0.5|x|? A) Vertical stretch B) Vertical shrink C) Horizontal shift D) Reflection Correct Answer: B) Vertical shrink 29. What happens when you reflect f(x) = |x| over the y-axis? A) Graph stays the same B) Graph shifts to the left C) Graph shifts down D) Graph flips over Correct Answer: A) Graph stays the same 30. Solve |x + 3| - 4 = 2. A) x = 2 or x = -4 B) x = 3 or x = -5 C) x = 1 or x = -7 D) x = 3 or x = -9 Correct Answer: C) x = 1 or x = -7