Math 107 Quiz 2 Spring 2017 OL4 Professor: Dr. Katiraie Name________________________________ Instructions: The quiz is worth 100 points. There are 10 problems, each worth 10 points. Your score will be posted in your Portfolio with comments. This quiz is open book and open notes, and you may take as long as you like on it provided that you submit the quiz no later than the due date posted in our course schedule of the syllabus. You may refer to your textbook, notes, and online classroom materials, but you may not consult anyone. You should show all of your work to receive full credit. If you do not show work, you may earn only partial or no credit. Please type your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is also acceptable. Be sure to include your name in the document. Review instructions for submitting your midterm exam in the Quizzes and Exams Conference. If you have any questions, please contact me by e-mail (farajollah.katiraie@faculty.umuc.edu). At the end of your quiz, you must include the following dated statement with your name typed in lieu of a signature. Without this signed statement you will receive a zero. I have completed this quiz myself, working independently and not consulting anyone except the instructor. I have neither given nor received help on this quiz. Name: Date: Please remember to show ALL of your work on every problem. If there is no work to show, then include a sentence or two explaining your answer. Here are the basic rules of showing work: a) Each step should show the complete expression or equation rather than a piece of it. b) Each new step should follow logically from the previous step, following rules of algebra. c) Each new step should be beneath the previous step. d) The equal sign, =, should only connect equal numbers or expressions. Our textbook is full of good models of work shown correctly. If you have questions about showing work, please ask. Math 107 Quiz 2 Page 2 Please Show or Explain Your Work on Each Problem. 1) Find the distance d between the points and the midpoint M of the line segment which connects them. (-3 , -10) , (-1 , -5) 2) Let's assume for a moment that we are standing at the origin and the positive y-axis points due North while the positive x-axis points due East. Our Sasquatch-o-meter tells us that Sasquatch is 5 miles East and 6 miles South of our current position. What are the coordinates of his position? How far away is he from us? If he runs 8 miles due West what would his new position be? 3) For the function below y=x 24 a) Find the x- and y-intercept(s) of the graph, if any exist b) Follow the procedure in Example 1.2.3 to create a table of sample points on the graph of the equation. c) Plot the sample points and create a rough sketch of the graph of the equation. d) Test for symmetry. If the equation appears to fail any of the symmetry tests, find a point on the graph of the equation whose reflection fails to be on the graph as was done at the end of Example 1.2.4 Math 107 Quiz 2 4) Page 3 For the following piecewise function, find the specified function values { 3 x for x <2 1 f ( x )= x+5 for2 4 2 102 for>4 a) f(-4) b) f (-2) c) f(0) d) f(4) e) f(10) 5) For the following pair of functions, f (x)=x +2, g (x)= x1 Find each of the following, and State its Domain: a) Find (f + g)(x) b) Find (f - g)(x) c) Find (f*g)(x) (Hint, this means f(x) times g(x)) d) Find (f*f)(x) (Hint: this means f(x) times f(x) e) Find (f/g)(x) (Hint: this means f(x) divided by g(x) Math 107 Quiz 2 f ( x+ h )f (x) h for the following function. (Hint: Please see page 79 in Section 1.5) 6) Find and simplify the difference quotient f ( x )=3 x7 f ( x+ h )f (x) h for the following function. (Hint: Please see page 79 in Section 1.5) 7) Find and simplify the difference quotient f ( x )=3 x2 7 f ( x+ h )f (x) h for the following function. (Hint: Please see page 79 in Section 1.5) 8) Find and simplify the difference quotient f ( x )= 5 x Page 4 Math 107 Quiz 2 Page 5 9) The cost, is C(x) = 4000 + 500x And the price-demand function, is p(x) = 2000 - 60x 1 x25 Where x is in thousands of computers, C(x) is in thousands of dollars, and p(x) denotes the wholesale price (in dollars) per computer at which x thousand computers can be sold. (Hint: Please see page 82 in section 1.5) Please answer the following: a) Find and interpret C(0). b) Find and interpret C(10). c) Find and interpret p(5) d) Find R(x). e) Find and simplify P(x). f) Solve P(x) = 0 and interpret. 10) The cost, is C(x) = 125 + 16x And the price-demand function, is p(x) = 75 - 3x 1 x20 Where x is in millions of chips, C(x) is in millions of dollars, and p(x) denotes the wholesale price (in dollars) per chip at which x millions chips can be sold. (Hint: Please see page 82 in section 1.5) Please answer the following: a) Find and interpret C(0). b) Find and interpret C(10). c) Find and interpret p(5) d) Find R(x). e) Find and simplify P(x). Math 107 Quiz 2 Page 6 End of Quiz 2: please do not forget to write and sign (or type) the required statement explained in the box above Part I of the Quiz 2