MATH 107 QUIZ 4 Fall 2016 Instructor: Dr.Kunhikrishnan Thengumthara NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. SIGNATURE: _______________________________ INSTRUCTIONS The quiz is worth 100 points. There are 10 problems covering week4&5 material. This quiz is open book and open notes. This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than Sunday, October2. Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work. General quiz tips and instructions for submitting work are posted in the Quizzes module. If you have any questions, please contact me by e-mail. 1. Find the following for the given polynomial function (16 points) f(x) = (2x - 3) (x+5)2 Degree of the polynomial Leading coefficient End behavior of diagram (Circle one) A. vvvv B. vvvv C. vvvv D. vvvv 2. (12 points) The graph represents which of the following equations? State the vertex : A. y = -x2 - 6x + 10 B. y = x2 + 6x + 10 C. State the Range: y = x2 + x - 37 D. y = -x2 - x + 37 3. Find all real zeros and their corresponding multiplicity of the following polynomial: (6points) P(x) = x3 ( 7x+5) 4. Use the Intermediate Value Theorem to prove that f(x) = x3 + 2x + 5 has a real zero in in the interval [-2, -1] 5. Let f ( x) x 2 3x (no explanations required) (16 points) x 2 36 (a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote. 6. What is the equation of the function whose graph is given below. Give explanation. (4 points) A. B. C. D. x 3 x2 8 f ( x) 2 x 4 x2 f ( x) x 1 x2 f ( x) x2 f ( x) 7. Find all complex solutions of the following equation(6points) 5x2 + 9 = 6x 8. Find and simplify the following (6points) (1 + 5i) (2 - 3i) 9. Solve the rational inequality. Express your answer using interval notation. (6points) x4 3 x2 10. Refer example 2.3.3 (page196) in your text book to do this problem. The marketing research department of a company that manufactures and sells laptops has the following Revenue and cost functions R(x) and C(x) respectively. (24 points) R(x)= - 60x2 + 2000x 1 x 25 where x is the number of laptops in thousands. C(x) = 500x + 4000 a) Find the equation of Profit function P(x) b) The shape of the graph of P(x) is a ........................... c) Find the maximum profit. d) Find the number of laptops sold when there is maximum profit. e) If p(x) = 2000 - 6x where p(x) is the price laptop (in dollars) when x laptops are sold. What is the sale price of a laptop when the profit is maximum? f) Find and interpret the break-even points. Show algebraic work