Choose Only One Answer For Multiple Choice: Determine The DO
Choose Only One Answer For Multiple Choice1determine The Domain Of T
Choose only one answer for Multiple Choice. 1. Determine the domain of the function. · · All real numbers · · x > 1 · · x ≤ 1 · · All real numbers except . Determine the domain of the function. · All real numbers except -8, -3, and 2 · x ≥ 0 · All real numbers · x ≥ -3, x ≠. f(x) = 3x + 2; g(x) = 3x - 5 Find f/g. · (f/g)(x) = ; domain {x|x ≠- } · (f/g)(x) = ; domain {x|x ≠} · (f/g)(x) = ; domain {x|x ≠} · (f/g)(x) = ; domain {x|x ≠- } 4. Use your graphing calculator to graph f(x) = |x + 1| and determine where the function is increasing and decreasing. · Increasing x > -1; Decreasing x 1 · Increasing x -1 · Increasing x > 1; Decreasing x
Select true or false: The function -3(x + 2)(x - 5)3 > 0, when x 5. · · True · · False 6. f(x) = 2x + 6, g(x) = 4x2 Find (f + g)(x). · 8x3 + 24x · · 4x2 + 2x + 6 · -4x2 + 2x + . f(x) = ; g(x) = 8x - 12 Find f(g(x)). · f(g(x)) = 2 · f(g(x)) = · f(g(x)) = 2 · f(g(x)) = . Describe how the graph of y = x2 can be transformed to the graph of the given equation: y = x2 - 20 · · Shift the graph of y = x2 left 20 units. · · Shift the graph of y = x2 up 20 units. · · Shift the graph of y = x2 down 20 units. · · Shift the graph of y = x2 right 20 units. 9. Is the function of f(x) = |4x| + even, odd, or neither? · Even · Odd · Neither 10. State the domain of the rational function. f(x) = · All real numbers except -10 and 10 · All real numbers except 13 · All real numbers except 10 · All real numbers except -13 and . If and , then . · True · False 12. Find the limit of the function algebraically. · · Does not exist · · 7 · · 0 · · -. Find . · · 10 · 18 · Does not exist · · 10 or . Evaluate . · · · 0 · · −∞ · · ∞ · · Does not exist 15. Evaluate . · · · 1 · · 0 · · · · Does not exist 16. Evaluate · · ∞ · · -∞ · · 0 · · 17. Find the equation of the horizontal asymptote for the function, . · There is no horizontal asymptote. · y = 0 · y = 1 · y = x 18. Which of the following is false for ? · The x-axis is an asymptote of f(x). · x = -1 is not an asymptote of f(x). · x = 1 is an asymptote of f(x). · The y-axis is an asymptote of f(x). 19. To two decimal places, find the value of k that will make the function f(x) continuous everywhere. · 11.00 · -2.47 · -0.47 · None of these 20. Where is discontinuous? · f(x) is continuous everywhere · 1 · 1, 4 · . Is the function continuous? · Yes · No 22. List the discontinuities for the function f(x) = cot( ). · There are no discontinuities. · n( ), where n is an integer · n( ), where n is an integer · n( ), where n is an integer 23. Which of the following is true for ? · There is a removable discontinuity at x = 3. · There is a non-removable discontinuity at x = 3. · The function is continuous for all real numbers. 24. What is the instantaneous slope of y = at x = 5? · · · · 1 · · -1 · · 25. What is the average rate of change of y with respect to x over the interval [-2, 6] for the function y = 5x + 2? · · 5 · · 2 · · · · . What is the slope for the function y = -3x2 + 2 at the point x = 2? · -4 · -10 · -12 · The slope cannot be determined. 27. The surface area, S, of a sphere of radius r feet is S = S(r) = 4Ï€r2. Find the instantaneous rate of change of the surface area with respect to the radius r at r = 4. · · 32Ï€ · · 16Ï€ · · 64Ï€ · · 4Ï€ 28. A ball is thrown vertically upward from the top of a 100 foot tower, with an initial velocity of 10 ft/sec. Its position function is s(t) = -16t2 + 10t + 100. What is its velocity in ft/sec when t = 2 seconds? · · -32 · · -38 · · -54 · · . Using the graph of f(x) below, find . · · −5 · · −∞ · · 0 · · 1. Find . · Does not exist · 0 · · 31. What is ? · · ∞ · · 0 · · −4 · · −∞ 32. What is ? · · −6 · · 0 · · 1 · · Does not exist 33. Find the limit of the function by using direct substitution. · Does not exist · · 0 · · 5 · · -. Use your graphing calculator to evaluate . · · 0 · Ï€ · e3 · . Use your calculator to select the best answer below: · · does not exist · · 1 · · -1 · · . · · · · · · · · 2a 37. Find . · does not exist · 3 · 0 · 38. If and , then find . · · 64 · · -4 · · 16 · · . Evaluate . · · 0 · · does not exist · · 1 · · -. Evaluate . · · · · · · · · 41. Evaluate . · · 1 · · · · · · does not exist 42. If f is a continuous function with even symmetry and , which of the following statements must be true? I. II.There are no vertical asymptotes. III.The lines y = 10 and y = -10 are horizontal asymptotes. · · I only · · II only · · I and II only · · All statements are true. 43. What are the horizontal asymptotes of the function ? · · y = 1 only · · y = -1 only · · y = 0 · · y = -1 and y = . Which one or ones of the following statements is/are true? I. If the line y = 2 is a horizontal asymptote of y = f(x), then f is not defined at y = 2. II. If f(5) > 0 and f(6)
I. II. III. · II and III only · I and II only · I only · II only 51. Which of the following must be true for the graph of the function ? There is: I. a vertical asymptote at x = 3 II. a removable discontinuity at x = 3 III. an infinite discontinuity at x = 3 · I only · II only · III only · I, II, and III 52. What is the average rate of change of y with respect to x over the interval [-3, 5] for the function y = 2x + 2? · · 16 · · · · 2 · · 53. What is the instantaneous slope of y = at x = 3? · · · · · · · · 54. The height, s, of a ball thrown straight down with initial speed 32 ft/sec from a cliff 48 feet high is s(t) = -16t2 - 32t + 48, where t is the time elapsed that the ball is in the air. What is the instantaneous velocity of the ball when it hits the ground? · · 64 ft/sec · · 0 ft/sec · · 256 ft/sec · · -64 ft/sec 55. The surface area of a right circular cylinder of height 5 feet and radius r feet is given by S(r)=2Ï€rh+2Ï€r2. Find the instantaneous rate of change of the surface area with respect to the radius, r, when r = 6. · · 24Ï€ · · 34Ï€ · · 64Ï€ · · 20Ï€ 56. Use your graphing calculator to evaluate . · · 1 · · · · Ï€ · · . Describe the discontinuity for the function . · · There is a hole at x = -9. · · There is a vertical asymptote at x = 3. · · There is a removable discontinuity at x = 3. · · There is no discontinuity at x = 3. 58. Find . · · does not exist · 2 · . Evaluate . · · ∞ · · -∞ · · 0 · · -. Evaluate . · -2 · · 0 · -∞ 61. Which of the following is the graph of which function has y = -1 as an asymptote? · · y = ln(x + 1) · · 62. If is continuous at x = -4, find f(-4). · · 4 · · -4 · · 8 · · -. Where is discontinuous? · f(x) is continuous everywhere · x = -4 · x = -2 · x = -4 and x = . Where is discontinuous? · f(x) is continuous everywhere · x = -4 · x = -2 · x = -4 and x = . If f(x) is discontinuous, determine the reason. · f(x) is continuous for all real numbers · The limit as x approaches 1 does not exist · f(1) does not equal the limit as x approaches 1 · f(1) is not defined 65. If f(x) is a continuous function defined for all real numbers, f(-1) = 1, f(-5) = -10, and f(x) = 0 for one and only one value of x, then which of the following could be that x value? · · -6 · · -5 · · -4 · · . Use the graph below to list the x value(s) where the limits as x approaches from the left and right of those integer values(s) are not equal. _______________________________ 67. Find . You must show your work or explain your work in words. _______________________________ 68. Find . You must show your work or explain your work in words. _______________________________ 69. A ball's position, in meters, as it travels every second is represented by the position function s(t) = 4.9t2 + 350. What is the velocity of the ball after 2 seconds? Include units in your answer. _______________________________ 70. The cost in dollars of producing x units of a particular telephone is C(x) = x. (10 points) 1. Find the average rate of change of C with respect to x when the production level is changed from x = 100 to x = 103. Include units in your answer. 2. Find the instantaneous rate of change of C with respect to x when x = 100. Include units in your answer. _______________________________ 71. State the domain and range for the function f(x) = 2x2 - 7. _____________________________ 72. Show that the function f(x) = x3 + is even, odd, or neither. _____________________________ 73. Determine the equation of a line, in slope-intercept form, that passes through the points (3, 6) and (6, 8). ____________________________ 74. Write the equation of the function g(x) if g(x) = f(x - 2) +4 and f(x) = x3 + 2. _____________________________ 75. Identify the maximum and minimum values of the function y = 10 cos x in the interval [-2Ï€, 2Ï€]. Use your understanding of transformations, not your graphing calculator. _____________________________ Gentry Inc. is a mid-sized tech firm (200 employees and $300 million in revenue) and has been privately held since the firm’s inception ten years ago. The organization’s board of directors is keen on expanding the operations globally to take advantage of a growing market. Based on reports from the research and development team, the organization can increase its profitability metrics by 15 to 25% if it expands the operations to China, Japan, and Germany. Becoming a multinational organization will not be easy. To finance this expansion, the board of directors has decided to take the organization public and issue some bonds to raise an additional $50 million. The research team has already determined that the organization meets the financial requirements outlined by the Securities Exchange Commission. The goal is to maximize the Initial Public Offering (IPO), and the leadership must efficiently manage the capital, measure the risk of the investments, and ensure the financial metrics are robust relative to similarly sized organizations. Based on the concepts that you learned this week from the assigned videos and articles surrounding growth strategies for companies, make an initial assessment of whether Gentry should expand into China, Japan, and Germany all at one time or in a phased approach. Module 2 : In your assignment, recall the strategies that you discussed in this module’s discussion questions about the different types of financial investments companies use for growth. Include the advantages and disadvantages of expanding with debt and equity (using the information that you learned in this module’s materials). Module 3 : Based on the information that you learned about capital structure and budgeting, determine what the optimal capital structure should be for Gentry. You will need to determine how much equity (common stock) the company will offer in the IPO and how much debt the company should assume in their global expansion to meet the goal of $50 million. Determine what capital structure will work best with your initial assessment. Describe the structure using the ratios. Include the dollar amount of equity (common stock) the company should issue in the IPO and how much debt the company should use for this expansion to reach the $50 million goal. Explain your rationale. Module 4 : Based on the information that you learned about the different types of risk, scenario, and sensitivity analysis, you will be identifying the risks that will be associated with the IPO and global expansion. Using your readings from this module: Determine how each of the following risk exposures affects the international expansion of Gentry: transaction risk, translation risk, economic risk. Include how you would use sensitivity and scenario analysis to make your recommendation. Spell out the advantages and disadvantages of each method. Using the information that you have compiled over the past four modules, prepare your summary recommendation for Gentry Inc. and its plan to expand internationally. Remember that the company is trying to raise $50 million to expand via an IPO and debt issuance. Create a 10-15 slide presentation detailing your findings. Your recommendation should be 1-2 slides. Note that the title slide and reference slides are not included in the 10-15 total. Be sure to include academic references in your presentation as well as any charts or graphs to convey your financial information. Include a summary the deliverables from Modules 02-04 in the presentation. Your slides should flow as a cohesive presentation, not a patchwork of distinct pieces of information. Please be descriptive and detailed in your justification and calculations. Thank you. Let f be the function defined as follows: 1. If a = 2 and b = 3, is f continuous at x = 1? Justify your answer. 2. Find a relationship between a and b for which f is continuous at x = 1. Hint: A relationship between a and b just means an equation in a and b. 3. Find a relationship between a and b so that f is continuous at x = 2. 4. Use your equations from parts (ii) and (iii) to find the values of a and b so that f is continuous at both x = 1 and also at x = 2? 5. Graph the piece function using the values of a and b that you have found. You may graph by hand or use your calculator to graph and copy and paste into the document.