Math 107 Quiz 5 UMUC

MULTIPLE CHOICE QUESTIONS. (36 pts total, 3 pts each)

1. Determine log$ 32. A. 4 C. 5/2 B. 8 D. None of these.

2. Solve 19 − 3� = � − 3. A. No solution. C. 5 B. 11/2 D. −2, 5

3. Determine the domain of � � = �0 + � − 12. A. −∞, 4 ∪ (3, ∞) C. −∞, −4 ∪ [3, ∞) B. −∞, −3 ∪ [4, ∞) D. [−4,3]

4. For the function � � = 2� + 3, its inverse, �9: � , is: A. : 0;<= C. −2� − 3 B. 2� − 3 D. ;9= 0

5. The function graphed below has an inverse. T. True F. False

6. The domain of � � = : ;90 is: A. [2, ∞) C. (−∞, ∞) B. (2, ∞) D. −∞, 2 ∪ (2, ∞)

7. The domain of � � = 2 − �9; is: A. (−∞, 2] C. (−∞, ∞) B. [−2, ∞) D. −∞, 2

8. The range of � � = 2 − �9; is: A. (−∞, 2] C. (−∞, ∞) B. [−2, ∞) D. −∞, 2

9. The inverse of � � = 2 − �9; is: A. : 09?@A C. − ln : 09; B. −ln (2 − �) D. 2 + �;

10. The domain of � � = ln � + 2 is: A. (−2, ∞) C. (−∞, ∞) B. (−∞, −2] D. −∞, −2

11. The range of � � = ln(� + 2) is: A. (−2, ∞) C. (−∞, ∞) B. (−∞, −2] D. −∞, −2

12. Which of the following best describes this graph? A. It is the graph of an absolute value relation. B. It is the graph of a function and it is one-to-one. C. It is the graph of a function and it is not one-to-one. D. It is not the graph of a function. SHORT ANSWER QUESTIONS. (24 pts total, 3 pts each)

Questions 13, 14, 15 and 16 involve the functions graphed below. Determine each, or state that it cannot be found using the information given. 13. (� ∘ �)(4) 14. (� ∘ �)(4) 15. (� ∘ �)(2) 16. (� ∘ �)(1) 17. Rationalize the denominator: : 0<= 18. Rationalize the numerator: 0 0 5.1 Function Composition 371 50. (g ! g)("2) 51. (g ! f)("2) 52. g(f(g(0))) 53. f(f(f("1))) 54. f(f(f(f(f(1))))) 55. (g ! g ! ··· ! g) | {z } n times (0) In Exercises 56 - 61, use the graphs of y = f(x) and y = g(x) below to find the function value. x y 1234 1 2 3 4 y = f(x) x y 1234 1 2 3 4 y = g(x) 56. (g ! f)(1) 57. (f ! g)(3) 58. (g ! f)(2) 59. (f ! g)(0) 60. (f ! f)(1) 61. (g ! g)(1) 62. The volume V of a cube is a function of its side length x. Let’s assume that x = t + 1 is also a function of time t, where x is measured in inches and t is measured in minutes. Find a formula for V as a function of t. 63. Suppose a local vendor charges $2 per hot dog and that the number of hot dogs sold per hour x is given by x(t) = "4t 2 + 20t + 92, where t is the number of hours since 10 AM, 0  t  4. (a) Find an expression for the revenue per hour R as a function of x. (b) Find and simplify (R ! x) (t). What does this represent? (c) What is the revenue per hour at noon? 64. Discuss with your classmates how ‘real-world’ processes su