MATH 107 QUIZ 3 NAME: _______________________________ September, 2017 Instructor: 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 Sunday, September 17. 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 )=104| x| . (no explanation required) (a) State the zero(s) of the function. ________ (b) Which of the following is true? 2. ______ A. f is an odd function. B. f is an even function. C. f is both odd and even. D. f is neither odd nor even. 3. (6 pts) Which of the following equations does the graph represent? Show work or explanation. 3. ______ A. y= 2 x+ 4 3 B. y= 3 x+ 4 2 C. 3 y= x +4 2 D. 2 y= x +4 3 4. (12 pts) Consider the points (2, -5) and (-2, 1). (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. (10 pts) A ball is thrown vertically upward with an initial velocity of 40 feet per second from the top of a 130-foot high tower. The height h in feet at t seconds after the ball's release is given by h(t) = -16t2 + 40t + 130 feet for 0 t 4.4 seconds. (a) What was the height of the ball 2 seconds after the ball's release? Show work. (b) Find and interpret the average rate of change of h over the interval [2, 4]. Show work. 6. (16 pts) Lisa wants to purchase large custom-made bumper stickers to advertise her business. Two websites offer different deals: Website A: Pay a fee of $48.00, plus $0.60 per bumper sticker or Website B: Pay a fee of $69.00, plus $0.45 per bumper sticker (a) State a linear function f (x) that represents Website A's total charge for an order of x bumper stickers. (b) State a linear function g(x) that represents Website B's total charge for an order of x bumper stickers. (c) Lisa wants to purchase 200 custom-made bumper stickers, as cheaply as possible. At which website should she place her order? Show work/explanation. (d) For what number of bumper stickers is the total charge exactly the same at both websites? Show algebraic work/explanation to solve for the answer. (e) Fill in the blanks: Website A is the cheaper option if ________(choose less or more) than ______ (enter number) bumper stickers are ordered. 7. (7 pts) A graph of y = f (x) follows. No formula for f is given. 7. _______ Which graph (A, B, C, or D) represents the graph of y = f (x + 1) 2 ? BRIEFLY EXPLAIN how you have decided which graph is the correct one. (Grid supplied for scratch work; You are NOT required to submit your own graph) y = f(x) -4 4 4 2 2 2 -2 4 -4 -2 -2 -4 -4 GRAPH A (below) -4 4 4 2 2 2 -2 4 -4 -2 -2 -2 -4 -4 4 2 4 2 4 GRAPH D (below) 4 4 2 2 2 -2 2 GRAPH B (below) GRAPH C (below) -4 -2 4 -4 -2 -2 -2 -4 -4 8. (20 pts, no explanation required) Consider the graph of the function y = f (x) pictured below. (a) State the value of f (1). (b) State the domain of the function. (c) State the range of the function. (d) State the x-intercept(s), if any. (e) State the y-intercept(s), if any. (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. (17 pts) Based on diabetes data from http://www.cdc.gov/diabetes/statistics/prev/national/figbysex.htm, the following chart shows the percentage of American males who have diagnosed diabetes, 1990-2011. Prevalence of Diagnosed Diabetes for Males 8 7 6 f(x) = 0.21x - 424.61 R = 0.98 5 Percentage of American males with diabetes 4 3 2 1 0 1985199019952000200520102015 Year The line of best fit, the regression line, is y = 0.2146 x 424.61, where x = year and y = percentage of American males with diagnosed diabetes. The value of r2 is 0.983. (a) Use the regression line to estimate the percentage of American males with diagnosed diabetes in 1995, to the nearest tenth. Show some work. (b) Use the regression line to estimate the percentage of American males with diagnosed diabetes in 2009, to the nearest tenth. Show some work. (c) Assuming the linear trend continues, in what year (to the nearest year) does the regression line predict the percentage of American males with diagnosed diabetes to be 8.0%? Show algebraic work, solving an appropriate equation. (d) 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. (e) What is the value of the correlation coefficient, r (rounded to 4 decimal places)? 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