Math_112_Fall_2010.jkovalsky.Lesson_09_-_Graphs_of_Functions

Math_112_Fall_2010.jkovalsky.Lesson_09_-_Graphs_of_Functions...

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Unformatted text preview: JORDAN KOVALSKY Math - 112 Spring 2010 WeBWorK Assignment Lesson 09 - Graphs of Functions Due Date: 09/27/2010 at 11:59pm CDT. The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making some kind of mistake. You can use the Feedback button on each problem page to send e-mail to the course instructors. 1. (1 pt) Here is the graph of the function g(x) = x3 . Part (a): ? (Click on the image to enlarge it.) Specify the y-coordinate of the point P on the given function. Give an exact expression. In the graph I put -pi/2 instead of - ; 2 Remember that = 3.14159 . . .. Exact value = Correct Answers: -pi**3/8 Part (b): ? 2. (1 pt) Use the vertical line test to determine whether each graph represents a function y = f (x). (Click on an image to enlarge it.) 1 Domain : Range : Part (c): ? Correct Answers: [-4,4] [-3,2] 4. (1 pt) Specify (using interval notation) the domain and range of the function given by the graph below. Part (d): ? y y n y Correct Answers: Domain : Range : 3. (1 pt) Specify (using interval notation) the domain and range of the function given by the graph below. Correct Answers: [-4,5] [-2,2) 2 5. (1 pt) Refer to the graph of the function F in the figure below. Find F(4). F(4) = Find F(-1). F(-1) = Is F(-4) positive? ? For which value of x is F(x) = 5? x= Find F(5) - F(-3). F(5) - F(-3) = Which is larger, f (-2) or g(-2)? ? Compute f (0) - g(0). f (0) - g(0) = Which among the quantities f (1) - g(1), f (2) - g(2), and f (3) - g(3) is the smallest? ? For which value(s) of x does g(x) = f (1)? x= Is the number 4 in the range of f or in the range of g? ? Correct Answers: Correct Answers: 3 0 y -6 0 g 5 2 -2, 3 f 6. (1 pt) Refer to the graph of the functions f and g in the figure below. 7. (1 pt) Refer to the graph of the functions f and g in the figure below. 3 10. (1 pt) Sketch the graph of the following function: |x| if x 0 y= 2 x if x > 0 Submit your graph to your instructor. 11. (1 pt) Below is the graph of the function g(x) = - 1 - x2 For the interval [0, 3], is the quantity g(x) - f (x) positive or negative? ? For the interval (-3, -2), is the quantity g(x) - f (x) positive or negative? ? Correct Answers: neg pos 8. (1 pt) Sketch the graph of the following function: B(x) = 1 - x2 1/x if - 1 x < 1 if x 1 Submit your graph to your instructor. Determine the coordinates of the given points P, Q and R in each figure; give an exact expression. Assume that each black line is parallel to one of the coordinate axes. Enter the exact values (no decimal points!). Type sqrt() for . Exact value of coordinates of P (No decimals) = ( , ) Exact value of coordinates of Q (No decimals) = ( , ) Exact value of coordinates of R (No decimals) = ( , ) 9. (1 pt) Sketch the graph of the following function: x3 C(x) = if x < 1 if x > 1 4 x Submit your graph to your instructor. Correct Answers: 2/5 -sqrt(1-(0.4)**2) -sqrt(1-(0.4)**2) -sqrt(1-(0.4)**2) -sqrt(1-(0.4)**2) -2/5 12. (1 pt) What is the definition of the average rate of change of a function g on an interval [c, d]? What does this have to do with slope? Submit your answer to your instructor. y Compute the Average Rate of Change of the function y = x f (x) = x on the interval [1, 9]. y = x Correct Answers: 2 / 8 15. (1 pt) 13. (1 pt) Compute the Average Rate of Change The following graph is a function with domain [0, 4]. f (x) = x3 - x on the interval [2, 3]. y = x y of the function y = x Correct Answers: 18 / 1 16. (1 pt) Iodine-131 is a radioactive substance. The following graph shows how an initial one-gram sample decays over a 32-day period; f (t) represents the number of grams present after t days. Specify: The range : The maximum value : The minimum value : The intervals where the function is increasing : The intervals where the function is decreasing : In the last two parts separate the intervals with commas. Correct Answers: [-2,2] 2 -2 [0,1], [2,3] [1,2], [3,4] (Click on the image to enlarge it.) Compute the Average Rate of Change f /t over each of the indicated intervals: 5 14. (1 pt) ( f /t) from t = 0 days to t = 8 days: grams / day ( f /t) from t = 8 days to t = 16 days: grams / day ( f /t) from t = 16 days to t = 24 days: grams / day ( f /t) from t = 24 days to t = 32 days: grams / day Find the average of the previous four answers. Average = grams / day Compute f /t over the interval from t = 0 to t = 32. Is the answer the same as that obtained in the previous question? ( f /t) from t = 0 days to t = 32 days: grams / day ? Correct Answers: 7+h 2*z+h+1 f (3 + h) - f (3) = h f (z + h) - f (z) = h 19. (1 pt) Find the difference quotient -3x + 6. f (x)- f (a) x-a f (x) - f (a) for the function f (x) = x-a f (x + h) - f (x) for the function h = Find the difference quotient f (x) = -3x + 6. f (x+h)- f (x) = h Correct Answers: -0.0625 -0.03125 -0.015625 -0.0078125 -0.029296875 -0.029296875 Y Correct Answers: -3 -3 20. (1 pt) 17. (1 pt) Let f (x) = 5x2 . f (x) - f (-4) Find . x+4 f (x)- f (-4) = x+4 f (x) - f (a) Find . x-a f (x)- f (a) = x-a Correct Answers: 5*[x+(-4)] 5*(x+a) Recall that the function s(t) = 16t 2 relates the distance s(t) and the time t for a freely falling object (neglecting air resistance). The time t is measured in seconds, with t = 0 corresponding to the instant that the object begins to fall; the distance s(t) is in feet. Find the average velocity over each of the following time intervals: [2, 3], [3, 4], and [2, 4]. Average Velocity[2,3] = Average Velocity[3,4] = Average Velocity[2,4] = Let a, b, and c denote the three average velocities, in the order given. Is it true that the arithmetic average of a and b is c? ? 18. (1 pt) Find and simplify the indicated difference quotient for the function f (x) = x2 + x: c Generated by the WeBWorK system WeBWorK Team, Department of Mathematics, University of Rochester Correct Answers: 80 112 96 y 6 ...
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