Concept explainers
In Exercises 13–24, calculate the 5-unit moving average of the given function. Plot the function and its moving average on the same graph, as in Example 4. (You may use graphing technology for these plots, but you should compute the moving averages analytically.) [HINT: See Quick Example 3 and Example 4.]
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Chapter 14 Solutions
Student Solutions Manual for Waner/Costenoble's Finite Math and Applied Calculus, 7th
- Part IV. If f is a one-to-one function with the following properties: f (3) = 13, f(21) = 4, f-1(5)%3D1, and f(2) = 8. Graph the function f.arrow_forward4. Working with functions. In this question, we will explore various properties of functions. You may want to review the basic definitions and terminology introduced on pages 15–16 of the course notes. Then, read the following definitions carefully. Definition: A function f : A → B is one-to-one iff no two elements of A have the same image. Symbol- ically, Va1, a2 E A, f(a1) = f(a2) → a1 = a2. (3) Definition: A function f: A → B is onto iff every element of B is the image of at least one element from A. Symbolically, VbE В, За Е А, f (a) — b. (4) Definition: For all functions f : A → B and g : B → C, their composition is the function g o f : A → C defined by: Va e A, (go f)(a) = g(f(a)). (5) (b) Give explicit, concrete definitions for two functions f1, f2 : Z → Z† such that: i. f2 is onto but not one-to-one, ii. fi is one-to-one but not onto, and prove that each of your functions has the desired properties.arrow_forwardIs this statement TRUE or FALSE?Gaussian Elimination is the process of deriving a simple function from a set of discrete data pointsarrow_forward
- PART 1 Complete the given table for the function y = (2)x. x -2 -1 0 1 2 yarrow_forwardThe observed values of a function are respectively 168, 120, 72 and 63 at (the four positions 3, 7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable ?arrow_forwardWhich of the following is NOT a function?arrow_forward
- The table shows the times it takes a certain model of car to accelerate from 0 mph to speeds of 30 mph, 40 mph, etc., up to 90 mph, in increments of 10 mph. Time (sec) Speed (mph) Time (sec) Speed (mph) 1.7 30 7.9 70 2.8 40 10.3 80 4.1 50 13.0 90 5.7 60 (a) Represent the times by x and the speeds by y. Which function type would be a reasonable choice to model these data? (Multiple Choice) A. power functioncubic function B. linear function C. quadratic function D. Any of these functions would be a reasonable choice. (b) Find the power function model for the data. (Round your coefficients to three decimal places.) y = ? (c) Graph the points and the function to see how well the function fits the points. (d) What does the model indicate the speed (in mph) is 5 seconds after the car starts to move? (Round your answer to the nearest integer.) ??? mph (e) According to the model, in how many seconds will the car reach 76.3 mph? (Round your…arrow_forwardUse Microsoft Excel to investigate the following function: f(x) = x³+x2-3x-1 Generate a table of ordered pairs for values of x ranging from -3 to +2. Use a step size of 0.2. You will have 26 x-values and 26 corresponding values of f(x). Insert an x,y scatter plot of the tabulated data into the worksheet. Use the graph to answer the following question. Which of the following are close to roots of the function (x-values for which the function is equal to zero)? Select one or more: a. -2.2 O b. -1.4 c. -0.4 O d. +0.8 O e. +1.4arrow_forward8arrow_forward
- Is this table a linear function ?arrow_forwardQUESTION 3 Determine whether or not f(x) is a function and select the best choice below to explain your reasoning. Fcx)3+1-30 O A. f(x) is not a function because it fails the horizontal line test. O B. f(x) is a function because it passes the horizontal line test. OC. f(x) is a function because it passes the vertical line test. O D. f(x) is not a function because it fails the vertical line test. 宇arrow_forwardLiberty Caner Name: Period: 5.2b Guided Practice: Linear and NonLinear Functions in Context 1. The following tables show the distance traveled by three different cars over five seconds. Provide Car 1 Car 2 Car 3 Time Distance Time Distance Time Distance (s) (ft.) (s) (ft.) (s) (ft.) 4 1 1 3 2 7 5 3 10 3 10 3 4 13 4 17 4 17 5 16 5 26 5 33 a. Consider the relationship between time and distance traveled for each car. Which of the tables of data can be modeled by a linear function? Which ones cannot be modeled by a linear function? Justify your answer. b. For any of the data sets that can be modeled by a linear function, write a function that models the distance traveled D as a function of time t. c. What is the dependent variable in this situation? The independent variable? d. Which car is traveling fastest? Justify your answer. on? Provide eviden 2. Hermione argues that the table below represents a linear function. Is she correct? How do you know? 2 8 16 y 1 Amki 3. Emily's little…arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell