The usefulness of graphs.

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1) This exercise illustrates limitations to the usefulness of graphs. Consider the function
f: R → R,
f (x) = {■(e^((-1)⁄x^2 )&x≠0@0&x=0)┤
Why is it reasonable to define f (0) = 0?
Using technology, construct a table of values, for the inputs {0, 0.1, 0.2, 0.3, 0.4}.
Using your answer to (b), attempt to construct a rough graph of f (x) over the interval
[0, 0.4].
What property of the function makes it so difficult to construct a meaningful graph?
Use technology (graphing calculator or computer algebra system) to graph f. Discuss your results.

2)
Let f be a function. Find a formula for the function whose graph is obtained from the graph of f by shifting two units to the left and then by stretching vertically by a factor of three. Then, find the function whose graph is obtained from the graph of f by stretching vertically by a factor of three and then by shifting two units to the left.
George and Laura are trying to graph 2sin(3x). Laura wants to do the horizontal compression followed by the vertical stretch, but George insists on the reverse order. Which method is correct? Why?
John wants to move up, and Teresa is willing to move to the left. Can they graph
sin⁡〖(x+π/4)+1〗? What two graphing transformations would they use? Does the order of
the transformations matter?
State a general principle about transformations, on the basis of parts (a), (b), and (c).

3) Suppose that the x -intercepts of the graph of f are {4,7}. Find the x -intercepts of the graphs of the following functions. (If it is impossible to tell from the given information, explain why.)
(a) f (x − 3)
(b) 2 f (7x + 1)
(c) 7 f (x) + 1

4) Let A be the set of all humans, and let B be the set of all human males. Define f: A → B by the rule f (a) = a ’s biological father.
(a) In words, describe the range of f.
(b) If y ∈ B, then (in words) what is the set f -1 [{y}]?
(c) If x ∈ A, then (in words) what is the set f^(-1)[ f [{x}]]?
(d) If y ∈ B, then what is the set f [ f^(-1) [{y}]]. Your answer should depend on whether y is in the range of f.
5) Let f: A → B be a function.
(a) Prove that if S ⊆ A, then f^(-1) [ f [S]] ⊇ S.
(b) Prove that if T ⊆ B, then f [ f^(-1) [T]] ⊆ T.
6) Let f : R R, f(x) = x^2 (x-3).
Given a real number b, find the number of elements in f^(-1) [{ b }]. (The answer will depend on b. It will be helpful to draw a rough graph of f, and you probably will need ideas from calculus to complete this exercise.)
Find three intervals whose union is R, such that f is injective as a function on each interval.
Use your answers to (a) and (b) to define the domain and codomain of three bijective function

7) Let F: R → R, F (x) = 3 x + 5. We can write F easily as the composite of two functions. Namely, if we define f and g (both with domain and codomain R ) by the rules f ( x ) = x + 5 and g ( x ) = 3 x , then F = f ◦ g . Find four other ways to write F as the composite of two functions (with domain and codomain R ).

Sample Solution

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Legislative Process

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Discuss a bill that is in the legislative process that interests you. Describe the bill, wherein the process (which committee) the bill is in, and who is supporting the bill. How will the policy impact your area of practice(
Nursing-FNP)? Even though it is your area of practice, keep your responses in the third person; in other words, how does the bill affect the ER, or school nursing, or education.

Sample Solution

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Diet Analysis Project

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Example of diet analysis from an analysis program (Chronometer was used): examples posted below. Click on the blue links for the daily analysis, average 3 day analysis, macro-nutrient analysis (with individual
carbohydrate, lipid/fat, protein), micro-nutrients (Vitamin and Minerals). Use the analysis to answer analyze your intake based against recommendations. Use the AMDR (Acceptable Macro-Nutrient Distribution Range) which was explained in the chapters at the beginning of the semester. Compare to the MyPlate
recommendations established by U.S. DEPARTMENT OF AGRICULTURE at www.myplate.gov (Links to an external site.). Use the Energy Balance assignment to compare the potential recommendation for your
individual needs against the diet analysis you obtained from your meals.
Remember: you need to provide copies of the analysis. You do not need to include all that are posted below
but at a minimum, provide each day (3 days) and the average of the 3 days.
Example of completed assignment sheet – see attached file (this is a real student example which has been modified and provided to get you thinking). You may notice that there are grammatical errors…please be
careful with your work.

Sample Solution

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Kendall Wallis

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PAIR A: ANSWER QUESTION 1 OR QUESTION 2 (FOUR POINTS)

  1. Why does Kendall Wallis ultimately decide to go along with Piasecki’s scheme?
    a. What personal, social, and economic factors (i.e., beyond the company) contribute to his decision?
    b. Compare Kendall Wallis with either Franz Brucher, the preteen protagonist of “The Balek Scales” (Böll, 1966; Week 6) or Munshi Vanshidhar, the eponymous protagonist of “The Salt Inspector” (Premchand, 2011/c. 1930; Week 6), in terms of the behaviors they take in response to their life circumstances, and what happens to them as a result of the behaviors.
  2. As Epley and Kumar (2019; Week 2) point out, “even well-meaning and well-informed people are more ethically malleable than one might guess” (p. 147). Epley and Kumar (2019) discuss four contextual factors that affect people’s behavior in organizations and therefore “need to be addressed when designing an ethical culture: explicit values, thoughts during judgment, incentives, and cultural norms” (p. 147). Account for Kendall’s behavior in terms of two of these factors.
    PAIR B: ANSWER QUESTION 3 OR QUESTION 4 (FOUR POINTS)
  3. Suppose that Kendall, before starting to work at Jimmy Dimon’s publishing house, had read and incorporated the advice of Kouchaki and Smith (2020; Week 6). Which specific recommendations in their article could have prevented Kendall’s unethical behavior?
  4. Suppose that Kendall, before agreeing to participate in Piasecki’s scheme, had studied Kahneman and Tversky’s concept of System 1 vs. System 2 thinking, as discussed by Bazerman (2020; Week 3) and Haugh (2017; Week 4). How might this knowledge have prevented Kendall from agreeing to the scheme?
    PAIR C: ANSWER QUESTION 5 OR QUESTION 6 (FOUR POINTS)
  5. Crossan, Côte, and Virgin (2020; Week 5) advise using character as a criterion for selecting leaders. Arguably, character is important not only for leaders, but for all members of organizations. Indeed, Smith and Kouchaki (2020; Week 5) tell us to take advantage of opportunities in the workplace to develop our character.
    a. To what extent would you attribute Kendall’s participation in the embezzlement to his character? Explain.
    b. How can people strengthen their character to become less susceptible to contextual pressures?
     
  6. Dimon, who made his fortune in the pornography business, is described as a “libertine.”

a. To what extent is he therefore necessarily an immoral leader? Tie your answer to two of the following articles: Bazerman (2000; Week 3), Bower (2020; Week 3), and Hirsh, Zyglidopoulos, and Alekos (2020, Week 5).
b. Refer to the Ppt for Week 5 and the article by “No author” (2015; Week 5). How do you expect Dimon, given his character deficiencies and excesses, to respond when he learns that his employees have been embezzling from him? Why?

PAIR D: ANSWER QUESTION 7 OR QUESTION 8 (FOUR POINTS)

  1. Haugh (2017; Week 4) discusses “eight rationalizations most commonly used by those committing unethical and illegal acts within companies” (Haugh, 2017; Week 4).

a. Which of these did Kendall use to rationalize what he did?
b. What other rationalization(s) did he use?

  1. Suppose that Dimon, upon discovering that his employees have been embezzling from him, reads Haugh (2017; Week 4), decides that having a second accountant is an inadequate ethics and compliance program, and hires you as a behavioral consultant. What specific suggestions will you give him to reduce his employees’ rationalization going forward?

PAIR E: ANSWER QUESTION 9 OR QUESTION 10 (FOUR POINTS)

  1. When Kendall begins to reap the financial benefits of his and Piasecki’s scheme, he also becomes a more productive employee. Why? What are the implications for those who design organizational ethics and compliance programs?
  2. At the end of the story, Kendall learns that Dimon is far more alert and perceptive than he and Piasecki had thought. What do you think Kendall will do after getting off the phone with Dimon? Why? What do you think will happen to him? Do you think he deserves such an outcome? Why (not)?

Name 1: Name 3:
Name 2: Name 4:

Did you answer ONE question from each pair?
Pair A B C D E

TOTAL
Question 1 2 3 4 5 6 7 8 9 10
Score

Sample Solution

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