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In Problems 43–52, evaluate
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- In Problems 6–11, find the domain of each functionarrow_forwardIn Problems 49–56, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Identify any local maximum values or local minimum values.arrow_forwardIn Problems 49–56, for each graph of a function y = f(x), find the absolute maximum and the absolute minimum, if they exist. Identifyany local maximum values or local minimum values.arrow_forward
- In Problems 94–97, the graphs of the given pairs of functions intersectinfinitely many times. In each problem, find four of these points ofintersection.arrow_forwardIn Problems 13–24, determine whether the graph is that of a function by using the vertical-line test. If it is, use the graph to find:(a) The domain and range (b) The intercepts, if any (c) Any symmetry with respect to the x-axis, the y-axis, or the originarrow_forwardIn Problems 31–42:(a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function.(d) Based on the graph, find the range. (e) Is f continuous on its domain?arrow_forward
- In Problems 19–26, sketch the graph of each function. Be sure to label three points on the grapharrow_forward1. In the figure below, find the number(s) "c" that Rolle's Theorem promises (guarantees). 10 For Problems 2–4, verify that the hypotheses of Rolle's Theorem are satisfied for each of the func- tions on the given intervals, and find the value of the number(s) "c" that Rolle's Theorem promises. 2. (a) f(x) = x² on |-2, 2 (b) f(x) = x² =5x +8 on [0,5] 3. (a) f(x) = sin(x) on [0, 7] (b) f(x) = sin(x) on [A,57]| 4. (a) f(x) = r-x+3 on | 1,1] (b) f(x) = x cos(x) on (0, [0, 1arrow_forwardIn Problems 23–30, use the given zero to find the remaining zeros of each function. 23. f(x) = x - 4x² + 4x – 16; zero: 2i 24. g(x) = x + 3x? + 25x + 75; zero: -5i 25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i 26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i %3D 27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i 29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i 28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i 30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3iarrow_forward
- In Problems 19–22, construct a polynomial function f that has the given properties. There is no unique answer. 19. f is of degree 4, its graph is symmetric with respect to the y-axis, y-intercept is (0, –6)arrow_forwardIn Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) any values of x that need to be excluded. = x. Give 27. f(x) = 3x + 4; g(x) = (x- 4) 28. f(x) = 3 – 2x; g(x) = -(x – 3) 29. f(x) = 4x – 8; 8(x) = + 2 30. f(x) = 2x + 6; 8(x) = ;x - 3 31. f(x) = x' - 8; g(x)· Vx + 8 32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2 33. f(x) = ; 8(x) = 34. f(x) = x; g(x) x - 5 2x + 3' 2x + 3 4x - 3 3x + 5 35. f(x) *: 8(x) = 8(x) 36. f(x) = 1- 2x x + 4 2 - x 1.7 82 CHAPTER 1 Graphs and Functions In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as a hint), the graph of y = x is also given. 37. y= X 38. 39. y =X 3 (1, 2), (0, 1) (-1,0) (2. ) (2, 1) (1, 0) 3 X (0, -1) -3 (-1, -1) 3 X -3 (-2, -2) (-2, -2) -하 -하 -하 40. 41. y = x 42. y = X (-2, 1). -3 3 X (1, -1)arrow_forwardEach of Exercises 31–36 gives a function ƒ(x), a point c, and a positivenumber P. Find L = lim xSc ƒ(x). Then find a number d 7 0 suchthat for all x0 < x - c < d => ƒ(x) - L < P. ƒ(x) = -3x - 2, c = -1, P = 0.03arrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
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