MATH 107 QUIZ 3 September, 2017 Instructor: I. Izmirli 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 10 problems. Each problem is worth 10 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, July 9. 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. For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin? (a) (b) Symmetric with respect to the x-axis? ____ y-axis? ____ origin? ____ 2. Let f ( x )=|3 x +1|7 . (a) State the zero(s) of the function. ________ (b) Which of the following is true? ______ A. f is an even function. B. f is an odd function. C. f is both even and odd. D. f is neither even nor odd. Symmetric with respect to the x-axis? ____ y-axis? ____ origin? ____ 3. Which of the following equations does the graph represent? ______ A. y= 4 x+ 8 3 B. y= 3 x+ 6 4 C. 3 y= x +6 4 D. 4 y= x +6 3 4. Consider the points (- 3, 7) and (3, -1). (a) Find the slope-intercept equation of the line passing through the two given points. (b) Graph the line you found in (a), either drawing it on the grid in the previous problem #3, or generating the graph electronically and attaching it. (c) Compare your line for this problem, #4, with the line in the previous problem #3. Are the two lines parallel, perpendicular, or neither parallel nor perpendicular? (The terms parallel and perpendicular are discussed on pages 166 and 167.) 5. The number of birds g in a water park t hours after 9 am is given by g(t) = -32t2 + 232t + 288 for 0 t 8. Here t = 0 corresponds to 9 am. Find and interpret the average rate of change of g over the interval {t | 3 t 6} = [3, 6]. 6. A business wants to purchase custom-made mugs for advertisement. Two companies offer different deals: Company A: Pay a design fee of $65.00, plus $4.25 per mug or Company B: Pay a design fee of $88.00, plus $4.00 per mug (a) State a linear function f (x) that represents Company A's total charge for an order of x mugs. (b) State a linear function g(x) that represents Company B's total charge for an order of x mugs. (c) If the business needs 110 custom-made mugs, as cheaply as possible, with which company should they place the order? 7. A graph of y = f (x) follows. No formula for f is given. _______ Which graph (A, B, C, or D) represents the graph of y = f (x 1) 1 ? y = f (x) 4 2 -4 -2 2 4 2 4 22 44 -2 -4 GRAPH A (below) -4 GRAPH B (below) 4 4 2 2 2 -2 4 -2 -2 -2 -4 -4 GRAPH C (below) -4 -4 GRAPH D (below) 4 44 2 22 2 -2 4 -4-4 -2-2 -2 -2-2 -4 -4-4 8. Consider the graph of the piecewise function y = f (x) pictured below. (a) State the value of f (4). (b) State the x-intercept(s), if any. (c) State the y-intercept(s), if any. 9. Consider the graph of the piecewise function y = f (x) pictured below. (a) State the domain of the function. (b) State the range of the function. 10. For the function defined in problem 9, (a) State the interval(s) on which the function is increasing. (b) State the interval(s) on which the function is decreasing