Mid Term Review I. Foundation of Functions Find the inverse of: 1. y = 11x + 6 2. y = 3x 21 Use compositions to determine if these functions are inverses: 4. f(x) = 4x + 9 and g(x) = x 9 5. f(x) = 2x + 10 and g(x) = 1 x + 5 2 4 Answer the following word problems. 6. A student bought concert tickets online. The cost, c in dollars, of tickets, t, can be found using the function c = 25t + 13.50. If the student spent a total of $88.50 on this ticket purchase, how many tickets did he buy? 7. The Spanish Club is ordering t-shirts online. The cost, c in dollars, of t-shirts, t, can be found using the function c = 11t + 27. If the club spent a total of $159.00 on this t- shirt order, how many t-shirts did the club buy?
Use the following graph for #8-9. The graph shows the relationship between the number of students who are sleeping and the number of minutes since class started. 8. What does the x-intercept of the graph represent? 9. What does the y-intercept of the graph represent? Use the following table for #10-11. Lily is driving a car at a constant speed. The table below shows the total number of miles driven as a function of the hours spent driving. Hours Spent Miles Driven Driving 2 114 4 228 6 342 10. Based on the data in the table, how many miles has Lily driven in 7 hours? 11. Based on the data in the table, how many miles has Lily driven in 8 hours? Which function below represents the data in the table? 12. 13. x Y x y 1 7 1 1.5 2 9 2 5 3 11 3 8.5 4 13 4 12 5 15 5 15.5 A. y = 2x + 5 B. y = 2(5 x ) C. y = 2x 2 + 5 D. y = 1 2 x+5 A. y = 3.5x 2 2 B. y = 3.5(2 x ) C. y = 2x-3.5 D. y = 3.5x 2
II. Absolute value equations and inequalities 14. Graph the absolute value function 15. Graph the absolute value function f(x) = 1 x 4 + 5 f(x) = 1 x + 2 4 4 2 16. Analyze the domain of the absolute value function. 17. A. {x x < 5} Write the domain and range of B. {x < x < } the above absolute value function C. {x x 5} D: D. {x 7 x 10} R:
Analyze the range of the absolute value function: 18. f(x) = x + 2 + 4 A. y 4 B. y < 2 C. y 4 D. y < 2 19. f(x) = x 8 11 A. y 11 B. y < 11 C. y 11 D. y < 8 20. Which of the following absolute value functions have a maximum? I. f(x) = x 3 2 II. f(x) = 1 2 x + 5 III. f(x) = x 1 IV. f(x) = 1 4 x 3 A. I and III B. II and III C. II only D. I and IV 21. Which of the following absolute value functions have a minimum? I. f(x) = x 3 2 II. f(x) = 1 2 x + 5 III. f(x) = x 1 IV. f(x) = 1 4 x 3 A. I and IV B. II and III C. IV only D. All of the above 22. Fill in the blank: The absolute value parent function is symmetric about the -axis. 23. Which function represents the graph? 24. Write the function which represents the graph? A. y = x 2 10 B. y = x + 2 + 10 C. y = x 10 + 2 D. y = x + 10 2
25. While playing pool, you try to shoot the eight ball into the corner pocket as shown. Imagine that a coordinate plane is placed over the pool table. The eight ball is at (5, 5 4 ) and the pocket you are aiming for is at (10, 5). You are going to bank the ball off the side at (6, 0). Show all the work when writing the absolute value function that represents the path of the ball. 26. Solve: 4x 5 = 7 27. Solve: 3 x + 11 = 6 28. Solve: 10x 15 = 25 A. 30, 50 B. -50, 30 C. -1, 1 D. -4, 4 29. Solve: x + 3 + 8 = 14 A. -2, 2 B. -9, 3 C. 19, 25 D. No solution
30. Solve the following inequality: 2x 4 + 5 < 11 A. x < 1 or x > 5 B. x < 5 C. 1 < x < 5 D. 2 < x < 4 31. Solve the following inequality: 4x + 4 + 2 > 14 A. x < 4 or x > 2 B. x > 4 C. 4 < x < 2 D. x = 4 III. Quadratic equations and inequalities 32. Write a function that has a vertex of (2,4) and contains the point (4,16). 33. Write a function that has a vertex of (-4,-2) and contains the point (-2,18). 34. Given the vertex and point, find the equation of the function
35. Given the vertex and point, find the equation of the function 36. Solve the quadratic equation using the square root method: (x 3) 2 + 15 = 45. 37. Solve the quadratic equation using the square root method: (x + 5) 2 + 12 = 76. 38. Solve the quadratic equation using the square root method: 5x 2 + 56 = 156. 39. Solve the quadratic equation using the square root method: 2x 2 36 = 132.
40. Which statement about the quadratic equation is true? 5.5x 2 + 198 = 0 A. The equation has a x=6 as its only solution B. The equation has no real solutions. C. The equation has x = 6 and x = -6 as its only solutions D. The equation has an infinite number of solutions. 41. Which statement about the quadratic equation is true? 6.5x 2 + 416 = 0 E. The equation has a x=8 as its only solution F. The equation has no real solutions. G. The equation has x = 8 and x = -8 as its only solutions H. The equation has an infinite number of solutions. 42. Solve the quadratic by factoring: x 2 8x + 12 = 0. 43. Solve the quadratic by factoring: 3x 2 + 24x + 45 = 0. 44. Solve and give the answer in interval notation: x 2 10x + 24 > 0. 45. Solve and give the answer in interval notation: x 2 12x + 35 > 0.
46. The graph of the quadratic function f is shown on the grid below. What does the solution set for f(x) = 0 appear to be? A. B. C. D. 47. The graph of the quadratic function f is shown on the grid below. What does the solution set for f(x) = 0 appear to be? A. B. C. D.