MATH 107 - 6981 QUIZ 2 Fall, 2016 Instructor: J. Thomas 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. 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, October 2. 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. (A) (4 pts) Which of these graphs of relations describe y as a function of x? That is, which are graphs of functions? (Note: There may be more than one graph which represents a function.) (B) (C) (D) 2. (10 pts) Consider the points (-5, -6) and (-1, 10). a) State the midpoint of the line segment with the given endpoints. (No work required) b) If the point you found in (a) is the center of a circle, and the other two points are points on the circle, find the length of the radius of the circle. (That is, find the distance between the center point and a point on the circle.) Find the exact answer and simplify as much as possible. Show work. 3. (12 pts) Consider the following graph of y = f (x). (no explanations required) (a) State the xintercept(s). (b) State the yintercept(s). (c) State the domain. (d) State the range. 4. (8 pts) Let f ( x) 2x 5 x 2 2 a) Evaluate f (3) b) Find the domain of the function: f ( x) 2x 5 x 2 2 c) Find f (a+5) and simplify as much as possible. Show your work. 2 5. (7 pts) Let f ( x )=x . Find and simplify the formula for a function graph is the result of f (1) (2) (3) (3) g( x) whose undergoing the following sequence of transformations. Horizontal shift 2 units to the right Reflection across x-axis Horizontal stretch by a factor of 3 Vertical shift up 1 unit 6. (6 pts) Given f ( x )=x5 of the quotient function f /g and g ( x ) =|x+ 7| , which of the following is the domain ? a) (7, ) b) (,7 ) (7, 5 ) (5, ) c) (7, 5 ) ( 5, ) d) (,7 ) (7, ) 7. (6 pts) For income x (in dollars), a particular state's income tax T (in dollars) is given by { 0.028 x if 0 x 2,500 T ( x )= 70+0.035(x2500) if 2,500< x 7,500 245+0.050(x7,500) if x> 7,500 a) What is the tax on an income of $6,300? Show some work. b) What is the tax on an income of $63,000? Show some work. 8. (20 pts) Let y=2 x 22 a) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional) b) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional) c) Create a table of sample points on the graph of the equation (include at least six points), and create a graph of the equation. (You may use the grid shown below, handdraw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and attach.) x y (x, y) d) Is the graph symmetric with respect to the y-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. e) Is the graph symmetric with respect to the x-axis? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. f) Is the graph symmetric with respect to the origin? _____ (yes or no). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook. 9. (12 pts) Let f (x) = 4x2 + 2x - 8 and g(x) = 1 - 2x. a) Evaluate the function g - f for x = -3. That is, find (g - f)(-3). Show work. b) Evaluate the function fg for x = -3. That is, find (f g)( -3). Show work. c) Find the difference function (f - g)(x) and simplify the results. Show work. 10. (15 pts) (See textbook page 82 for definitions of the economic functions used in this problem.) The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for x 0, and the price-demand function, in dollars per widget, is p(x) = 45 0.02x for 0 x 2250. a) Find and interpret C(300). b) Find and interpret C (300). (Note that C (x) is the average cost function.) c) Find and simplify the expression for the revenue function R(x). (work optional) d) Find and simplify the expression for the profit function P(x). (work optional) Note that p(x) and P(x) are different functions. e) Find and interpret P(300), where P(x) is the profit function in part d)