College Algebra MATH 107 Spring, 2017, V1.13 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. 1. ______ 4 2 -4 2 -2 4 -2 -4 A. B. C. D. Domain (- , 4]; Range (- , 2] Domain [- 2, 2]; Range [- 2, 4] Domain [- 2, 4]; Range [-2, 2] Domain [0, 3]; Range [0, 2] 2. Solve: 15 + 2x = x A. B. C. D. 2. ______ No solution -3 -5 -3, 5 Page 1 of 11 College Algebra MATH 107 Spring, 2017, V1.13 3. Determine the interval(s) on which the function is increasing. A. (-, -2) B. (- 5.5, -2) C. (-2, 3) D. (- 4, 1) 3. ______ 4. Determine whether the graph of y = x + 3 is symmetric with respect to the origin, the x-axis, or the y-axis. 4. ______ A. symmetric with respect to the y-axis only B. symmetric with respect to the x-axis only C. symmetric with respect to the origin only D. not symmetric with respect to the y-axis, not symmetric with respect to the x-axis, and not symmetric with respect to the origin 5. Solve, and express the answer in interval notation: A. B. C. D. 7 2x 9 . 5. ______ [-1, 8] [-1, ) (-, 8] [-1, ) (-, -1] [8, ) Page 2 of 11 College Algebra MATH 107 Spring, 2017, V1.13 6. Which of the following represents the graph of 4x 9y = 36 ? A. B. C. D. 6. ______ Page 3 of 11 College Algebra MATH 107 Spring, 2017, V1.13 7. Write a slope-intercept equation for a line parallel to the line x + 3y = 8 which passes through the point (- 4, 5). 7. ______ A. 1 11 y = x+ 3 3 B. 1 y = x+5 3 C. y= D. y = 3x 7 1 x+5 3 8. Which of the following best describes the graph? A. B. C. D. 8. ______ It is not the graph of a function. It is the graph of an absolute value function. It is the graph of an exponential function. It is the graph of a logarithmic function. Page 4 of 11 College Algebra MATH 107 9. Express as a single logarithm: 6 log x + log 1 - log y A. log ( 6 x + 1 y ) B. log ( x 6 + 1 y ) C. x6 log y D. x +1 log y Spring, 2017, V1.13 9. ______ 6 10. Which of the functions corresponds to the graph? 10. ______ A. f ( x ) = e x + 3 B. f ( x ) = e x + 3 C. f ( x ) = e x + 4 D. f ( x ) = e x + 4 Page 5 of 11 College Algebra MATH 107 Spring, 2017, V1.13 11. Suppose that for a function f , the equation f (x) = 0 has exactly two real-number solutions. Which of the following statements MUST be true? A. B. C. D. f f f f 11. ______ is a quadratic function is an invertible function. has exactly two x-intercepts. has exactly two y-intercepts. 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. ______ -4 4 4 2 2 2 -2 4 -4 2 -2 -2 -2 -4 -4 y = f (x) 4 y = g(x) A. B. C. D. g(x) = f (x + 1) - 2 g(x) = f (x - 1) - 2 g(x) = f (x + 2) + 2 g(x) = f (x + 1) - 1 Page 6 of 11 College Algebra MATH 107 Spring, 2017, V1.13 SHORT ANSWER: 13. Multiply and simplify: (8 + 3i)(5 + 7i). Write the answer in the form a + bi, where a and b are real numbers. 14. Solve, and write the answer in interval notation: x+9 0. x4 Answer: ________ Answer: ________ 15. Water initially at 185 F. is left in a room of temperature 70 F to cool. - 0.096 t After t minutes, the temperature T of the water is given by T(t) = 70 + 115e Find the temperature of the water 20 minutes after it is left to cool. (Round to the nearest degree.) Answer: ________ 1 16. Find the value of the logarithm: log 4 . 64 17. Solve: 75x4 = 49 . Answer: ________ Answer: ________ 18. Suppose $3,300 is invested in an account at an annual interest rate of 9.2% compounded continuously. How long (to the nearest tenth of a year) will it take the investment to double in size? Answer: ________ 2 19. Let f (x) = x 6x + 7. (a) Find the vertex. Answer: ________ (b) State the range of the function. Answer: ________ (c) On what interval is the function decreasing? Answer: ________ Page 7 of 11 College Algebra MATH 107 Spring, 2017, V1.13 20. Consider the polynomial P(x), shown in both standard form and factored form. 1 3 3 13 1 P ( x) = x 4 + x3 x 2 x + 3 = ( x + 2)( x 1)( x 3)( x 4) 8 4 8 4 8 (a) Which sketch illustrates the end behavior of the polynomial function? B. A. vvvv C. vvvv D. vvvv vvvv Answer: ________ (b) State the y-intercept. Answer: ________________ (c) State the zeros of the function. Answer: ________________ Answer: ________ (d) State which graph below is the graph of P(x). GRAPH A GRAPH B GRAPH C GRAPH D Page 8 of 11 College Algebra MATH 107 21. Let f ( x) = Spring, 2017, V1.13 2+ x . 3 x (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 f ( x ) = 2+ x ? 3 x GRAPH A. GRAPH B. GRAPH C. GRAPH D. Answer: ______________ Page 9 of 11 College Algebra MATH 107 Spring, 2017, V1.13 SHORT ANSWER, with work required to be shown, as indicated. 22. Let f ( x) = x 6 and g(x) = x 9. f (a) Find (15) . Show work. g (b) Find the domain of the quotient function f . Explain. g 23. Points (6, - 8) and (9, 1) 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 (7, 8) and (9, - 4). Write the equation in slope-intercept form. Show work. 25. A salesperson earns a base salary of $2,100 per month and a commission of 5.8% on the amount of sales made. If the salesperson has a paycheck of $4,211.20 for one month, what was the amount of sales for the month? Show work. 2 26. Let f (x) = 7x + 5 and g(x) = x - 2. (a) Find the composite function ( f o g )( x) and simplify. Show work. (b) Find ( f o g ) (1) . Show work. 2 27. Find the exact solutions and simplify as much as possible: 10x 1 = 2x. Show work. 28. Given the function f ( x) = 1 x 5 , find a formula for the inverse function. Show work. 6 Page 10 of 11 College Algebra MATH 107 Spring, 2017, V1.13 29. The fuel efficiency F for a particular car is given by F(x) = -0.02 x2 + 1.56 x + 9.8 where x is the speed of the car in miles per hour (mph) and F(x) is the corresponding fuel efficiency in miles per gallon (mpg). (a) What is the fuel efficiency if the car's speed is 65 mph? (b) What speed will yield the maximum fuel efficiency? Show work. 30. Solve: x3 20 = 2 . Show work. x+2 x 4 Page 11 of 11 Math 107 Final Examination Spring, 2017 1 Math 107 College Algebra Name______________________________ Final Examination: Spring, 2017 Instructor __________________________ Answer Sheet Instructions: 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. Record your answers and work in this document. There are 30 problems. Problems #1-12 are multiple choice. Record your choice for each problem. Problems #13-21 are short answer. Record your answer for each problem. Problems #22-30 are short answer with work required. When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plaintext formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages. You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement. Please sign (or type) your name below the following honor statement: I have completed this 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___________________ Math 107 Final Examination Spring, 2017 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) (c) 20. (a) (b) (c) (d) 21. (a) (b) (c) (d) 2 Math 107 Final Examination Spring, 2017 SHORT ANSWER with Work Shown. Record your answers and work. Problem Number Solution Answers: (a) (b) Work/for part (a) and explanation for part (b): 22 Answers: (a) (b) (c) Work for part (a): 23 3 Math 107 Final Examination Spring, 2017 Answer: Work: 24 Answer: Work: 25 Answers: (a) (b) Work for part (a) and for part (b): 26 4 Math 107 Final Examination Answer: Work: 27 Answer: Work: 28 Spring, 2017 5 Math 107 Final Examination Answers: (a) (b) Work for (b): 29 Answer: Work: 30 Spring, 2017 6