2. Find the midpoint between the two points and. a. (3, -6) b. (-1, -13) c. d. e.
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1 Precalculus with Limits (Larson 2 nd ed.) Chapter 1 Mid-Term Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Find the distance between the two points and. a. 153 b. 99 c. 102 d. 51 e Find the midpoint between the two points and. a. (3, -6) b. (-1, -13) c. d. e. 3. Write the standard form of the equation of the circle with the given characteristics. center: ; radius: 4 a. b. c. d. e.. 4. Write the standard form of the equation of the circle with the given characteristics. center: ; solution point: a. b. c. d. e.. 5. Find the center and radius of the circle. a. center:, radius: 10 b. center:, radius: 12 c. center:, radius: 12 d. center:, radius: 10 e. center:, radius: Find the center and radius of the circle. a. center:, radius: 49 b. center:, radius 7 c. center:, radius 7 d. center:, radius 7 e. center:, radius What is the domain of the function? a. b. c. d. e. 8. What is the domain of the function? a. b. c. d. e.
2 9. What is the domain and range of the function that is graphed below? a. Domain: ( 7, 6), Range: [ 6, 6] b. Domain:, Range: [ 6, 6] c. Domain: [ 7, 6], Range: [ 6, 6] d. Domain: [ 7, 6], Range: e. Domain: [ 6, 6], Range: [ 7, 6] 10.What is the average rate of change of the function f (x) = 3x 7 between x = 2 and x = 3? a. 0 b. 4 c. 2 d. 6 e What is the average rate of change of the function between? a. -10 b. -2 c. -4 d. -8 e Suppose the graph of f is given. Describe how the graph of the function can be obtained from the graph of f. a. Shift the graph of to the right 4 units, stretch vertically by a factor of 5, and then shift downward 3 units. b. Shift the graph of to the left 4 units, stretch vertically by a factor of 5, and then shift downward 3 units. c. Shift the graph of to the right 5 units, stretch vertically by a factor of 4, and then shift downward 3 units. d. Shift the graph of to the left 5 units, stretch vertically by a factor of 4, and then shift upward 3 units. e. Shift the graph of to the left 5 units, stretch vertically by a factor of 4, and then shift downward 3 units. 13. Use and to evaluate f(g( 1)). a. -2 b. 6 c. -28 d. -7 e Is the line through points P(0, 5) and Q( 1, 8) parallel to the line through points R(3, 3) and S(5, 1)? Explain. a. No, the lines have unequal slopes. b. Yes; the lines are both vertical. c. Yes; the lines have equal slopes. d. No, one line has slope, the other has no slope.
3 15. Which two lines are parallel? I. II. III. a. I and II c. II and III b. I and III d. No two of the lines are parallel. 16. Is the line through points P(0, 9) and Q(2, 8) perpendicular to the line through points R(1, 4) and S(3, 3)? Explain. a. Yes; their slopes are equal. b. Yes; their slopes have product 1 c. No; their slopes are not opposite reciprocals. d. No; their slopes are not equal. 17. A man is running around a circular track 200 m in circumference. An observer uses a stopwatch to time each lap, obtaining the data in the table as follows: What was the man's average speed (rate) between 68 s and 168 s? a. 4 m/s b m/s c. 3 m/s d. 8m/s e. 5 m/s Time (s) Distance (m) The graph shows the depth of water W in a reservoir over a one-year period, as a function of the number of days x since the beginning of the year. What was the average rate of change in W between x = 100 and x = 200? a b c. 0.2 d e If, find an equation for. a. b. c. d. e. 20. What is the distance between the center of the circle the vertex of the parabola? a. 4 b. 6 c. 2 d. 8 e. 10
4 Short Answer 21. Evaluate the function,, at the specified value of the independent variable and then simplify. 22. Find the domain of the function. 23. Describe the sequence of transformations from the related common function to g. 24. Describe the sequence of transformations from the related common function to g. 25. Write an equation for the function that is described by the following characteristics: the shape of the x-axis, but moved eight units down, two units to the left, and then reflected in 26. Find ( f + g)(x) when and. 27. Find ( f / g )(x) when and. 28. Evaluate the indicated function for and. Find( fg )(1). 29. Find when and 30. Find when and 31. Evaluate if 32. Given and Find [Hint: ] 33. Find the inverse function of f.
5 34. A pair of points is graphed. (a) Find the distance between them. (b) Find the midpoint of the segment that joins them. 35. Find the domain of the function. 36. Find the domain of the function. 37. Use and to evaluate the expression. (a) (b) 38. Use and to evaluate the expression. (a) (b) 39. Find the domain and range of the inverse of each function. a. b. 40. Is, with vertices at P(3, 3), Q(2, -2), and R(0, 1), a right triangle? 41. Use the graph of the function to find the domain and range of f.
6 Use the graph to determine the domain and range of the relation, and state whether the relation is a function. y y x x 44. Use the graph to determine the domain and range of the function and state whether the function has an inverse. y x Given and Find [Hint: ] 46. Are the lines parallel, perpendicular, or neither? a. b. c. d. 47. A rock is dropped off the edge of a cliff. After 2 seconds, the rock fell 25 ft. After 4 seconds the rock fell 65 ft from the edge. What is the average rate of falling per second? 48. Find each of the following given that and. a. ( f + g )(2) b. ( f g )(2) c. ( fg )(2) d. ( f /g )(2)
7 Chapter 1 Mid Term Exam Review Answer Section MULTIPLE CHOICE 1. D 2. A 3. D 4. C 5. C 6. C 7. D 8. A 9. C 10. E 11. A 12. E 13. A 14. A 15. A 16. C 17. A 18. E 19. C 20. D SHORT ANSWER all real numbers 23. horizontal shift 4 units right; then vertical stretch by a factor of reflection in the x-axis; then vertical shift 6 units up ( f + g)(x) = ; (1, 2) ; ; domain: [0, ), range: [, ) 40.Yes 41.domain: domain: [0, ), range: [3, ) range: 42. Domain: [-3, 7] 43. Domain: [0, ) Range: [-7, 3] Range: (- ) No, it fails the vertical line test. No, it fails the vertical line test. 44. Domain: (- ) Range: [-1, 1] No, it is not one-to-one. It fails the horizontal line test and does not have an inverse. 46. a. perpendicular b. parallel c. neither d. perpendicular ft/sec 48. a. 3 b. 7 c. -10 d. -5/2
3. parallel: (b) and (c); perpendicular (a) and (b), (a) and (c)
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