University of Maryland University College MATH 107 QUIZ 3 NAME: _______________________________ Summer, 2017 Instructor: Dr. J. Wulu 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. 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 Monday, June 19. 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. (6 pts) For each graph, is the graph symmetric with respect to the x-axis? y-axis? origin? (No explanation required. Just answer Yes or No to each question.) (a) (b) Symmetric with respect to the Symmetric with respect to the x-axis? ____ x-axis? ____ y-axis? ____ y-axis? ____ origin? ____ origin? ____ 2. (6 pts) Let f ( x )=2|x|3 . (no explanation required) (a) State the zero(s) of the function. ________ (b) Which of the following is true? 2. ______ 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. 3. (6 pts) Which of the following equations does the graph represent? Show work or explanation. 3. ______ 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. (12 pts) Consider the points (- 2, 5) and (7, -3). (a) Find the slope-intercept equation of the line passing through the two given points. Show work. (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.) No explanation required - just state the answer. 5. (8 pts) The number of guests g in a water park t hours after 9 am is given by g(t) = -32t2 + 224t + 263 for 0 t 8. (t = 0 corresponds to 9 am) Find and interpret the average rate of change of g over the interval {t | 3 t 5} = [3, 5]. Show work. 6. (20 pts) Luke wants to purchase custom-made mugs to advertise his business. Two companies offer different deals: Company A: Pay a design fee of $60.00, plus $5.50 per mug or Company B: Pay a design fee of $82.00, plus $4.20 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) Luke wants to purchase 150 custom-made mugs, as cheaply as possible. With which company should he place his order? Show work/explanation. (d) For what number of mugs is the total charge exactly the same for both companies? Show algebraic work/explanation. (e) Fill in the blanks: Company A is the cheaper option if ________(choose less or more) than ______ (enter number) mugs are ordered. 7. (8 pts) 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 ? EXPLAIN YOUR CHOICE. (Grid supplied for scratch work; You are NOT required to submit your own graph) y = f (x) 4 2 - 4 2 -2 4 GRAPH A (below) 4 2 2 4 GRAPH C (below) - 4 2 -2 4 2 4 2 4 GRAPH D (below) 4 2 - 4 2 -2 4 2 4 GRAPH B (below) 4 2 - 4 2 -2 4 7. _______ 4 4 4 24 2 2 - -2 2 4 -2 4 2 4 2 4 8. (20 pts, no explanation required) Consider the graph of the piecewise function y = f (x) pictured below. (a) State the value of f (1). (b) State the x-intercept(s), if any. (c) State the y-intercept(s), if any. (d) State the domain of the piecewise function. (e) State the range of the piecewise function. (f) State the interval(s) on which the function is increasing. That is, for what x-values is the function increasing? (g) State the interval(s) on which the function is decreasing. That is, for what x-values is the function decreasing? 9. (14 pts) Life expectancy at birth is the estimated lifespan of a baby born in a particular year (given the conditions of that time period). Based on data retrieved from http://www.indexmundi.com/facts/united-states/life-expectancy-at-birth the following chart of U.S. life expectancy for males has been prepared. U.S. Male Life Expectancy at Birth 78 76 f(x) = 0.21x - 336.5 74 R = 0.98 72 70 Life Expectancy (in years) 68 66 64 62 60 1950 1960 1970 1980 1990 2000 2010 2020 Birth Year The regression line is y = 0.2052x - 336.5, where x = birth year and y = U.S. life male expectancy, in years. The value of r2 is 0.9809. (a) Use the regression line to estimate the U.S. life expectancy of a male baby born in 1985, to the nearest tenth of a year. Show some work. (b) Use the regression line to predict the U.S. life expectancy of a male baby born in 2010, to the nearest tenth of a year. Show some work. (c) What is the slope of the regression line and what are the units of measurement? In a sentence, interpret what the slope is telling us, in the context of this real-world application. (d) What is the value of the correlation coefficient, r? Also, interpret its value: Looking at the graph and the size of r, do you judge the strength of the linear relationship to be very strong, moderately strong, somewhat weak, or very weak