MATH 107 QUIZ 2 August, 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, September 10. 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. Which of these graphs of relations describe y as a function of x? That is, which are graphs of functions? Answer(s): ____________ (A) 2. Consider the points (B) ( 52 ,3) (C) and ( 12 , 4) (D) . (a) State the midpoint of the line segment with the given endpoints. (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. 3. Consider the following graph of y = f (x). (no explanations required) (a) State the x-intercept(s). (b) State the y-intercept(s). (c) State the domain. (d) State the range. 4. Let f ( x ) = x6 ( x4 )3 (a) Calculate f (2 ) . (b) State the domain of the function f ( x ) = x6 ( x4 )3 (c) Find f ( a+ 2 ) and simplify as much as possible. 5. f is a function that takes a real number x and performs these four steps in the order given: (1) Multiply by 2. (2) Add 4. (3) Take the cube root. (4) Take the reciprocal. (a) Find the expression for f (x). (b) State the domain of f. 6. Given f /g f ( x )=2 x7 and g ( x ) =|3 x4| , what is the domain of the quotient function ? 7. For income x (in dollars), a particular state's income tax T (in dollars) is given by { 0.02 4 x if 0 x 2,500 T ( x )= 6 0+ 0.033 ( x2500) if 2,500< x 7,500 22 5+0.05 1( x7,500) if x>7,500 (a) What is the tax on an income of $6,400? (b) What is the tax on an income of $66,000? 8. Let 2 y=x +3 x2 (a) Find the x-intercept(s) of the graph of the equation, if any exist. (b) Find the y-intercept(s) of the graph of the equation, if any exist. 9. (a) Create a table of sample points of the equation 2 y=x +3 x2 . Include at least six points, and create a graph of the equation. You may use the grid shown below, hand-draw 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) (b) 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. 10. Let f (x) = 6x2 + 3x - 11 and g(x) = 10 - 4x. (a) Evaluate the function g - f for x = -2. That is, find (g - f)(-2). (b) Evaluate the function fg for x = -2. That is, find (f g)( -2). Show work. (c) Find the difference function (f - g)(x) and simplify the results