# Math 107 Final ExaminationSummer, 20151Math 107 College Algebr.docx

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### Math 107 Final ExaminationSummer, 20151Math 107 College Algebr.docx

• 2. final examination myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this final examination. Name ____________ ______ ___ Date___________________ ) MULTIPLE CHOICE. Record your answer choices. 1.7. 2.8. 3.9. 4.10. 5.11. 6.12. SHORT ANSWER. Record your answers below. 13. 14. 15. 16. 17. 18. 19. (a) (b)
• 3. (c) 20. (a) (b) (c) (d) 21. (a) (b) (c) (d) SHORT ANSWER with Work Shown. Record your answers and work. Problem Number Solution 22 Answers: (a)
• 4. (b) Work/for part (a) and explanation for part (b): 23 Answers: (a) (b) (c)
• 5. Work for part (a): 24 Answer: Work:
• 7. (b) Work for part (a) and for part (b): 27 Answer: Work:
• 11. College Algebra MATH 107 Summer, 2015, V1.4 Page 1 of 11
• 12. MATH 107 FINAL EXAMINATION This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Record your answers and work on the separate answer sheet provided. There are 30 problems. Problems #1–12 are Multiple Choice. Problems #13–21 are Short Answer. (Work not required to be shown) Problems #22–30 are Short Answer with work required to be shown. MULTIPLE CHOICE 1. Determine the domain and range of the piecewise function.
• 13. 1. ______ A. Domain [–2, 4]; Range [–3, 3] B. Domain [–1, 2]; Range [0, 2] C. Domain [–1, 4]; Range [–2, 2] D. Domain [–3, 3]; Range [–2, 4] 2. Solve: 10 3x x− = − 2. ______
• 14. A. No solution B. 5 C. –5, 2 D. –5 -2 2 4 -4 -2 -4 2 4 College Algebra MATH 107 Summer, 2015, V1.4 Page 2 of 11 3. Determine the interval(s) on which the function is increasing.
• 15. 3. ______ A. (–∞, –1) B. (–∞, – 3) and (1, ∞) C. (– 2, 2) D. (– 4.5, – 1) and (2.5, ∞) 4. Determine whether the graph of 3y x= + is symmetric with respect to the origin, the x-axis, or the y-axis. 4. ______
• 16. A. not symmetric with respect to the x-axis, not symmetric with respect to the y-axis, and not symmetric with respect to the origin B. symmetric with respect to the x-axis only C. symmetric with respect to the y-axis only D. symmetric with respect to the origin only 5. Solve, and express the answer in interval notation: 7 4 5x− ≥ . 5. ______ A. [1/2, 3] B. (–∞, 3] ∪ [1/2, ∞) C. (–∞, 1/2] ∪ [3, ∞) D. [1/2, ∞) College Algebra MATH 107 Summer, 2015, V1.4
• 17. Page 3 of 11 6. Which of the following represents the graph of 4x + 9y = 36 ? 6. ______ A. B. C. D. College Algebra MATH 107 Summer, 2015, V1.4 Page 4 of 11
• 18. 7. Write a slope-intercept equation for a line parallel to the line x + 7y = 8 which passes through the point (–14, 6). 7. ______ A. 7 92y x= − − B. 1 8 7 y x= + C. 1 4 7 y x= − +
• 19. D. 1 6 7 y x= − + 8. Does the graph below represent a function and is it one-to- one? 8. ______ A. It is a function and it is one-to-one. B. It is a function but not one-to-one.
• 20. C. It is not a function and it is not one-to-one. D. It is not a function but it is one-to-one. College Algebra MATH 107 Summer, 2015, V1.4 Page 5 of 11 9. Express as a single logarithm: 2 log (x + 3) – 4 log y + log 1 9. ______ A. 6 log( ) log(4 ) x y
• 22. 3 log x y D. ( )log 2 7 4x y+ − 10. Which of the functions corresponds to the graph? 10. ______ A. ( ) 2 1xf x e−= −
• 23. B. ( ) 1xf x e−= + C. ( ) 2xf x e− += D. ( ) 2xf x e += − College Algebra MATH 107 Summer, 2015, V1.4 Page 6 of 11 11. Suppose that for a function f , the equation f (x) = 0 has exactly one real-number solution. Which of the following statements MUST be true? 11. ______ A. f has exactly one real-number zero. B. f is a linear function. C. f (x) ≥ 0 for all x in the domain of f. D. f is an invertible function.
• 24. 12. The graph of y = f (x) is shown at the left and the graph of y = g(x) is shown at the right. (No formulas are given.) What is the relationship between g(x) and f (x)? 12. ______
• 25. y = f (x) y = g(x) A. g(x) = f (x – 3) – 1 B. g(x) = f (x – 1) – 3 C. g(x) = f (x + 1) – 3 D. g(x) = f (x – 1) – 1 2 4 -2 -4 -2 -4 2
• 26. 4 2 4 -2 -4 -2 -4 2 4 College Algebra MATH 107 Summer, 2015, V1.4 Page 7 of 11 SHORT ANSWER: 13. Multiply and simplify: (6 + 5i)(8 + i). Write the answer in the form a + bi, where a and b are real numbers. Answer: ________
• 27. 14. Solve, and write the answer in interval notation: 4 0 2 x x + ≥ − . Answer: ________ 15. A bowl of soup at 165° F. is placed in a room of constant temperature of 75° F. The temperature T of the soup t minutes after it is placed in the room is given by
• 28. T(t) = 75 + 90 e – 0.075 t Find the temperature of the soup 20 minutes after it is placed in the room. (Round to the nearest degree.) Answer: ________ 16. Find the value of the logarithm: 3 1 log 9 . Answer: ________
• 29. 17. Solve: 5 87 49x + = . Answer: ________ 18. Suppose \$2,400 is invested in an account at an annual interest rate of 7.1% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ 19. Let f (x) = x 2 −−−− 4x + 7. (a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer:
• 30. ________ College Algebra MATH 107 Summer, 2015, V1.4 Page 8 of 11 20. Consider the polynomial P(x), shown in both standard form and factored form. 3 21 7 7 1 ( ) 5 ( 1)( 3)( 5) 3 3 3 3 P x x x x x x x= − + − − = − + − − (a) Which sketch illustrates the end behavior of the polynomial function? Answer: ________
• 31. (b) State the zeros of the function. Answer: ________________ (c) State the y-intercept. Answer: ________________ (d) State which graph below is the graph of P(x). Answer: ________ GRAPH A GRAPH B GRAPH C GRAPH D A. B. C. D. vvvv
• 32. vvvv vvvv vvvv College Algebra MATH 107 Summer, 2015, V1.4 Page 9 of 11 21. Let 2 2 3 3 ( ) 4 x f x x
• 33. − = − . (a) State the domain. Answer: _________________ (b) State the horizontal asymptote. Answer: _________________ (c) State the vertical asymptote(s). Answer: _________________ (d) Which of the following represents the graph of 2 2
• 34. 3 3 ( ) 4 x f x x − = − ? Answer: ______________ GRAPH A. GRAPH B. GRAPH C. GRAPH D.
• 35. College Algebra MATH 107 Summer, 2015, V1.4 Page 10 of 11 SHORT ANSWER, with work required to be shown, as indicated. 22. Let f (x) = x + 6 and xxg −= 3)( . g f
• 36. . Show work. (b) Find the domain of the quotient function g f . Explain. 23. Points (–3, 2) and (1, 8) are endpoints of the diameter of a circle. (a) What is the length of the diameter? Give the exact answer, simplified as much as possible. Show work. (b) What is the center point C of the circle? (c) Given the point C you found in part (b), state the point symmetric to C about the x-axis. 24. Find the equation for a line which passes through the points
• 37. (–6, 1) and (–8, 9). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of \$1,650 per month and a commission of 5.3% on the amount of sales made. If the salesperson has a paycheck of \$3425.50 for one month, what was the amount of sales for the month? Show work. 26. Let f (x) = 5x 2 – 8 and g(x) = x – 2. (a) Find the composite function ))(( xgf o and simplify. Show work. (b) Find ( ) ( 1)f g −o . Show work.
• 38. 27. Find the exact solutions and simplify as much as possible: 2x 2 + 3 = 6x. Show work. 28. Given the function 1 ( ) 7 3 f x x= + , find a formula for the inverse function. Show work. College Algebra MATH 107 Summer, 2015, V1.4 Page 11 of 11
• 39. 29. Donut Delights, Inc. has determined that when x donuts are made daily, the profit P (in dollars) is given by P(x) = –0.002 x 2 + 4.1x – 1350 (a) What is the company’s profit if 800 donuts are made daily? (b) How many donuts should be made daily in order to maximize the company’s profit? Show work.
• 40. 30. Solve: 2 5 28 7 49 x x x + = + − . Show work.
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