8/14 OL1 UMUC Math-107, Quiz #3 Instructor: Killough Instructions This quiz is worth 100 points. Individual point values for each problem are shown next to the problem number. The material is ONLY from weeks #4 and #5. 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, except for the instructor. The quiz will be available for 7 days. Students must submit their answers and detailed work by Sunday at midnight. Late exams will be penalized 10% per day. Students must submit all detailed work, where indicated. In some cases, there will be multiple choice or short answer solutions that do not require work. Answers without work may earn little or no credit, so if you are not sure, include your work. You may type or write your work in your copy of the quiz, or if you prefer, create a separate document containing your work. Scanned work is also acceptable. Be sure to include your name at the top of any submitted document. 1. (10 pts) Solve the inequality |42 x|8 and write the solution set in interval notation. Select one of the multiple choice answers. Show work. A. B. C. D. [-2, ) (-, -2] [6, ) (-, 6] [-2, ) [-2, 6] 2. (10 pts) Solve x +3 x1 0 and write the solution set in interval notation. Select one of the multiple choice answers. Show work. A. B. C. D. [-3, 1) (-, -3] (-, -3] (1, ) (1, ) 3. (10 pts) For f (x) = x3 + x2 - 4, use the Intermediate Value Theorem to determine which interval must contain a zero of f. Select one of the answers. Show work. A. B. C. D. Between 0 and 1 Between 1 and 2 Between 2 and 3 Between 3 and 4 8/14 OL1 4. (10 pts) Consider the graph of the quadratic function. Find the following: (a) State the vertex (b) State the range (c) State the interval on which the function is decreasing (d) Select which of these equations represents the graph. A. y = -x2 + 2x -1 B. y = -2x2 - 4x + 1 C. y = 2x2 + 4x -1 D. y = x2 + 2x - 1 5. (10 pts) Let 4x 2 4 f ( x) 2 x 9 . (no explanations required) (a) State the y-intercept. (b) State the x-intercept(s). (c) State the vertical asymptote(s). (d) State the horizontal asymptote. 6. (10 pts) Solve the equation. Check all proposed solutions. Show work. x 1 6 2 0 x 2 x 2x 7. (10 pts) Simplify the term 1+3 i 2i Write the result in the form a + bi, where a and b are real numbers. Show work. 8. (10 pts) Consider the equation 3x2 + 2 = 4x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work. 9. (10 pts) The cost (C) for a company to produce x widgets is given by C(x) = 5250 + 7.0 x. The company has determined that the profit (P) for x widgets is given by P(x) = 0.02 x2 + 38.0 x 5250. (a) What is the Cost (C) to produce 500 widgets and what is the Profit (P)? Show work. 8/14 OL1 (b) Find the vertex of the profit function P(x) using algebra. Your answer should be a point (x,P). Describe what this point represents? Show work. 8/14 OL1 10. (10 pts) Let ( 32 ) ( x4 ) P ( x )=( x +1 ) x P ( x )=x 3 +4.5 x 20.5 x6 When factored, (a) State the domain. (b) Which sketch illustrates the end behavior of the polynomial function? Select one answer. A. B. vvvv C. vvvv D. vvvv vvvv (c) State the y-intercept. (d) State the real zeros. (e) State which graph below is the graph of P(x). Select one answer. GRAPH A. (below) GRAPH B. (below) GRAPH C. (below) GRAPH D. (below) 8/14 OL1