State University of New York Compute the Values Algebra Questions

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♡ The homework is page 218 11,13,17,27 Page 232 25 37 39 43 red. ne with slope s x²-9 are have graphs that respect to X is required to guarante oth an absolute maxim y 10 5) 0, 1) (2, 10) (0, 0) 3 X 28. (5,0) (7.3 LO 29. 5 YA 2 T 2 (--/-/, -1) --²-- -4 (-2, 0) 45. g(x) = (-1/1, 1) 53. 2 FIN 1 4 YA -(0, 3) π.Χ. (2,0) 4 X (3, 3) (2, 2) 3 30. (2, 3) (-T, -1) (3, 2) In Problems 33-36, the graph of a function f is given. Use the graph to find: (a) The numbers, if any, at which f has a local maximum. What are the local maximum values? (b) The numbers, if any, at which f has a local minimum. What are the local minimum values? 33. YA 34. 35. (-1/2, 1) (5, 1) 5 (0,0) 2 46. h (x) T 3 (0, 2) 54. -2 4 -3 (-1,0) (1,0) 2- = (0, 1) In Problems 37-48, determine algebraically whether each function is even, odd, or neither. 37. f(x) = 4x³ 38. f(x) = 2x¹ - x² 39. g(x) = -3x² - 5 41. F(x)=√x 42. G(x) = √x 43. f(x) = x + |x| -x³ 3x² - 9 EN (0, 2) 2 X x² - 1 (1, 1) YA 4- (-1,3) (0, 2) π.Χ. (TT, -1) 59. f(x) = x³ x³ (-2,2) 61. f(x) = -0.2x³ - 0.6x² + 4x - 6 (-6,4) 63. f(x) = 0.25x4 + 0.3x³ -0.9x² + 3 (-3,2) 3 X (2,4) 2 (4,4) 3 31. (-3,2) (5,0) -3 5 (-1,2) (3.0) In 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. 50. 49. YA (1,4) 51. E 55. 47. h(x) 얘 (-1/2, -1) 3 YA 4 = 2 9 3 X (1,-1) (2, -1) (0, 3) (1, 1) (0, -/-) YA 2 SECTION 3.3 Properties of Functions 233 -1 (-2,-2) -2 TT -1 (3, 1) 3 (3, 4) (4,3) (2,0) ហ· 3 5 (3, 2) 32. (4,1) (-2.3, 0). 36. (-2,1) -3, (-3,-2) A (-, -1) --²-- 2x 48. F(x) = |x| 52. YA 56. 2 (0, 1) YA 3 40. h(x) = 3x³ + 5 44. f(x) = √√/2x² + 1 YA 2 (-1, 1) 2 -2 (1,3) (0, 1) (3,0) 3 X (2,4) (2, 2) 3 (1,3) (0, 2) π. Χ (π, -1) (-1,-3) In Problems 57-64, use a graphing utility to graph each function over the indicated interval and approximate any local maximum values and local minimum values. Determine where the function is increasing and where it is decreasing. Round answers to two decimal places. 58. f(x) = x³ - 3x² + 5 (-1,3) 57. f(x) = x³ - 3x + 2 (-2,2) 60. f(x) = x²-x² (-2,2) 62. f(x) = -0.4x³ + 0.6x² + 3x - 2 (-4,5) 64. f(x) = -0.4x4 -0.5x³+0.8x²-2 (-3,2) (3, 1) 1 (2,0) 3 000 98232 CHAPTER 3 Functions and Their Graphs 3.3 Assess Your Understanding 'Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 4. Write the point-slope form of the line with slope containing the point (3,-2). (p. 171) 1. The interval (2,5) can be written as the inequality (pp. 120-121) 5. The intercepts of the equation y = x-9 are (pp. 159-160) 2. The slope of the line containing the points (-2,3) and (3,8) is . (pp. 167-169) - 3. Test the equation y = 5x² - 1 for symmetry with respect to the x-axis, the y-axis, and the origin. (pp. 160-162) Concepts and Vocabulary 6. A function f is 10. True or False on an open interval I if, for any choice of x₁ and x₂ in I, with x₁ < x₂, we have f(x₁) f(x₂). 9. True or False A function f has a local maximum at c if there is an open interval I containing c such that for all x in I, f(x) ≤ f(c). Skill Building In Problems 13-24, use the graph of the function f given. 13. Is f increasing on the interval (-8, -2) ? 14. Is f decreasing on the interval (-8,-4)? 15. Is f increasing on the interval (−2, 6)? 16. Is f decreasing on the interval (2,5)? 17. List the interval(s) on which f is increasing. 18. List the interval(s) on which f is decreasing. 19. Is there a local maximum at 2? If yes, what is it? 20. Is there a local maximum at 5? If yes, what is it? 21. List the number(s) at which f has a local maximum. What are the local maximum values? 22. List the number(s) at which f has a local minimum. What are the local minimum values? 23. Find the absolute minimum of fon [-10, 7]. 24. Find the absolute maximum of fon [-10, 7]. 107 ods (-4,2) YA 4 In Problems 25-32, the graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which the function is increasing, decreasing, or constant (d) Whether the function is even, odd, or neither 25. 26. (-3, 3) -4 (-2,0) (0, 3) (4,2) (2,0) 4 X YA 3 (0, 2), 01 -3 (-1,0) (1,0) (3, 3) symmetric with respect to the origin. 11. An odd function is symmetric with respect to (a) the x-axis (b) the y-axis (c) the origin (d) the line y = x 12. Which of the following intervals is required to guarantee a continuous function will have both an absolute maxima and an absolute minimum? (a) (a, b) (b) (a, b] (c) [a, b) b (d) [a, b] 3 X 27. -10 (-10, 0) -3 mal (-5, 0) -5 (-8,-4) ya 3 Even functions have graphs that a (0, 1) (-2, 6) 3 X y 10 -6 28. (2,10) (0, 0) -3 (5,0) (7,3) 5 YA (1,0) SEP I In F 37. 41. 45. 53. In Pr. any lo 49. (-1 T In Proble. and local 57. f(x) 59. f(x) 61. f(x) 63. f(x)ne intersects in red. on the graph of the graph of the function ambers, is f(0). on in x and y, then the t satisfy the equation is e range of the function e relation of the function n have more than one of (c) both (d) neither af to answer parts (a)-(n). 0), (2) (5, 3) ive? ative? f? (x) = 0? (x) < 0? (6,0) pts? X (a) The domain and range In 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: (b) The intercepts, if any 14. (c) Any symmetry with respect to the x-axis, the y-axis, or the origin 16. 13. \17. -3 21. t? ne y = -1 intersect the graph? ne x = 1 intersect the graph? Des f(x) = 3? = oes f(x) = -2? 3 3 L (-1,2) 3) co 3 X 3 x (1,2) 18. 22. -3 -3 (1,³) -3 y 3 3 YA 3 3 X 3 X In Problems 25-30, answer the questions about the given function. 25. f(x) = 2x² - x - 1 (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -1, what is x? What point(s) are on the graph of f? 3 X (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 26. f(x) = -3x² + 5x (a) Is the point (-1,2) on the graph of f? (b) If x= -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 27. f(x) on the graph of f? x + 2 x-6 (a) Is the point (3, 14) on the graph of f? (b) If x= 4, what is f(x)? What point is on the graph of f? (c) If f(x) = 2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. x² + 2 x + 4 (a) Is the point 15. 19. 23. -3 -1 FINT L 9 6 30. f(x) y. 1 YA = 3- = FIN SECTION 3.2 The Graph of a Function = TT X (3,2) 24. NA 3 X (2, -3) -3 3 X 1 -T 20. 2 1 EN YA 4 (4,3) f -4 4 X 1 2' (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 2.x² (12,5) 29. f(x) x + 1 (a) Is the point (-1, 1) on the graph of f? (b) If x= 2, what is f(x)? What point is on the graph of f? (c) If f(x) = 1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 2x x-2 219 3 X (a) Is the point on the graph of f? 3, (b) If x= 4, what is f(x)? What point is on the graph of f? (c) If f(x) 1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f.218 CHAPTER 3 Functions and Their Graphs SUMMARY Graph of a Function The collection of points (x, y) that satisfies the equation y = f(x). Vertical-Line Test 3.2 Assess Your Understanding 'Are You Prepared?' Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 1. The intercepts of the equation x² + 4y² = 16 are (pp. 159-160) Concepts and Vocabulary 3. A set of points in the xy-plane is the graph of a function if line intersects the graph in at and only if every most one point. 4. If the point (5,-3) is a point on the graph of f, then f( = 5. Find a so that the point (-1,2) is on the graph of f(x) = ax² + 4. A collection of points is the graph of a function if and only if every vertical line intersects the graph in at most one point. 6. True or False Every graph represents a function. 7. True or False The graph of a function y = f(x) always crosses the y-axis.didW STAN Skill Building 11. Use the given graph of the function f to answer parts (a)-(n). 21 83 (-3,0) 10-5 4 (0, 3). (-5,-2) (-6,-3) (2,4) (4,3) 5 (6,0) (a) Find f(0) and f(-6). (b) Find f(6) and f(11). (c) Is f(3) positive or negative? (d) Is f(-4) positive or negative? (e) For what values of x is f(x) = 0? (f) For what values of x is f(x) > 0? (g) What is the domain of f? (h) What is the range of f? (i) What are the x-intercepts? (j) What is the y-intercept? (10,0) (11,1) 11 x (8,-2) to 2. True or False The point (-2,-6) is on the graph of th equation x = 2y - 2. (pp. 157-159) 1 (k) How often does the line y = intersect the graph? 2 (1) How often does the line x = 5 intersect the graph? (m) For what values of x does f(x) = 3? (n) For what values of x does f(x) = -2? 8. True or False The y-intercept of the graph of the function y = f(x), whose domain is all real numbers, is f(0). 9. If a function is defined by an equation in x and y, then the set of points (x, y) in the xy-plane that satisfy the equations called 10. The graph of a function y = f(x) can have more than one of which type of intercept? (a) x-intercept (b) y-intercept (c) both (d) neither NEOT pour tol a te Alumin (a) the domain of the function (b) the range of the function (c) the graph of the function (d) the relation of the function og Je 12. Use the given graph of the function f to answer parts (a 1202 9361976 ƏL (-4, 2) y -4 -2 4 (-2, 1) 2 (0,0) -2 (a) Find f(0) and ƒ(6). (b) Find f(2) and f(-2). (4,0), 4 2 (2,-2) (5, 3) (6,0) 1 6 X (c) Is f(3) positive or negative? (d) Is f(-1) positive or negative? (e) For what values of x is f(x) = 0? (f) For what values of x is f(x) < 0? (g) What is the domain of f? (h) What is the range of f? (i) What are the x-intercepts? (i) What is the y-intercept? graph (k) How often does the line y = -1 intersect the grant (1) How often does the line x = 1 intersect the g (m) For what value of x does f(x) 3? (n) For what value of x does f(x) = -27 In P 13. 17. 21. -3 (-1 Z3 In Problem 25. f(x) = (a) Is (b) If x (c) If j of J (d) Wh (e) List (f) List 26. f(x) = (a) Is th (b) If x= (c) If f( of f? (d) What (e) List t (f) List th 27. f(x) = x (a) Is the (b) If x= (c) If f(x) of f? (d) What is (e) List the (1) List the +² 28. f(x) x + (a) Is the po
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