MATH 107 QUIZ 2 April 2, 2017, Instructor: E.Avram NAME: _______________________________ I have completed this assignment myself, working independently and not consulting anyone except the instructor. INSTRUCTIONS The quiz is worth 100 points. There are 9 problems. Problem #8 has 20 points. 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, April 2. Show work/explanation. 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. Determine analytically if the following functions are even, odd or neither. 3 2 a. f(x) = x + x + x + 1 b. f(x) = 1x 2 Answers: a. neither b. even 2. Use the graph of y = f(x) given below to answer the questions. f(x) 6 4 2 -5 -4 -3 -2 -1 0 0 1 2 3 4 5 -2 -4 -6 a. Find the domain of f. b. Find the range of f. c. Determine f(2). d. Solve f(x) = 5. Answer: a. [4, 4] b. [5, 5) c. f(2)=3 d. x= -2 3. Sketch the graph of the given function. State the domain of the function, identify any intercepts and test for symmetry 2 a. f(x) = x + 1 b. f(x) = x(x 1)(x + 2) Answer: a. Domain: (, ) x-intercept: None y-intercept: (0, 1) Even b. Domain: (, ) x-intercepts: (2, 0), (0, 0), (1, 0) y-intercept: (0, 0) No symmetry 4. Find both the point-slope form and the slope-intercept form of the line with the given slope which passes through the given point. a. m = 1, P(7, 1) b. m = 678, P(1, 12) Answer: a. y + 1 = (x + 7) y = x - 8 b. y + 12 = 678(x + 1) y = 678x + 666 5. You are given a line and a point which is not on that line. Find the line perpendicular to the given line which passes through the given point. a. y = 6x + 5, P(3, 2) b. y = 6, P(3, 2) Answer: a. y = 1/ 6 x + 3/2 b. x = 3 6.Solve the equation : a. 2|5x + 1| 3 = 0 b. |2x 1| = x + 1 Answer: a. x = 1 /2 or x = 1/ 10 b. x = 0 or x = 2 7. Determine whether or not the equation represents y as a function of x. a. x 2 2 y =1 b. . y = Answer : a. Not a function x 2 +4 b. Function 8. Use the pair of functions f and g to find the following values if they exist. (f + g)(2) (f g)(1) (g f)(1) a.f(x) = 3x + 1 and g(x) = 4 - x 2 2 c.f(x) = x x and g(x) = 12 x (fg) (1/ 2) (f/ g) (0) b. f(x) = x x+3 ( g/ f) (2) and g(x) = 2x - 1 1 2 d. f(x) = x + 1 and g(x) = x 2 +1 9. Let f be the function defined by f = {(3, 4),(2, 2),(1, 0),(0, 1),(1, 3),(2, 4),(3, 1)} and let g be the function defined by g = {(3, 2),(2, 0),(1, 4),(0, 0),(1, 3),(2, 1),(3, 2)} . Compute the indicated value if it exists: a. (f + g)(3) b. (f g)(2) Answer: a.(f + g)(3) = 2 b. (f g)(2) = 3 c. (fg)(1) c. (fg)(1) = 0 d. (g + f)(1) d. (g + f)(1) = 0