{"id":10767,"date":"2015-07-10T19:40:02","date_gmt":"2015-07-10T19:40:02","guid":{"rendered":"https:\/\/courses.candelalearning.com\/osprecalc\/?post_type=chapter&p=10767"},"modified":"2021-10-25T02:54:15","modified_gmt":"2021-10-25T02:54:15","slug":"functions-and-function-notation-solutions","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ccbcmd-math-1\/chapter\/functions-and-function-notation-solutions\/","title":{"raw":"Solutions: Functions and Function Notation","rendered":"Solutions: Functions and Function Notation"},"content":{"raw":"

Solutions to Odd-Numbered Exercises<\/span><\/h2>\r\n1. A relation is a set of ordered pairs. A function is a special kind of relation in which no two ordered pairs have the same first coordinate.\r\n\r\n3. When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output. At any particular input value, there can be only one output if the relation is to be a function.\r\n\r\n5. When a horizontal line intersects the graph of a function more than once, that indicates that for that output there is more than one input. A function is one-to-one if each output corresponds to only one input.\r\n\r\n7. function\r\n\r\n9. function\r\n\r\n11. function\r\n\r\n13. function\r\n\r\n15. function\r\n\r\n17. function\r\n\r\n19. function\r\n\r\n21. function\r\n\r\n23. function\r\n\r\n25. not a function\r\n\r\n27. [latex]f\\left(-3\\right)=-11\\\\ f\\left(2\\right)=-1\\\\ f\\left(-a\\right)=-2a - 5\\\\-f\\left(a\\right)=-2a+5\\\\f\\left(a+h\\right)=2a+2h - 5[\/latex]\r\n\r\n29. [latex]f\\left(-3\\right)=\\sqrt{5}+5\\\\ f\\left(2\\right)=5\\\\ f\\left(-a\\right)=\\sqrt{2+a}+5\\\\ -f\\left(a\\right)=-\\sqrt{2-a}-5\\\\f\\left(a+h\\right)=\\\\sqrt{2-a-h}+5[\/latex]\r\n\r\n31. [latex]f\\left(-3\\right)=2\\\\f\\left(2\\right)=1 - 3=-2\\\\f\\left(-a\\right)=|-a - 1|-|-a+1|\\\\ -f\\left(a\\right)=-|a - 1|+|a+1|\\\\\\text{ }\\text{ }f\\left(a+h\\right)=|a+h - 1|-|a+h+1|[\/latex]\r\n\r\n33. [latex]\\frac{g\\left(x\\right)-g\\left(a\\right)}{x-a}=x+a+2,x\\ne a[\/latex]\r\n\r\n35. a. [latex]f\\left(-2\\right)=14[\/latex]; b. [latex]x=3[\/latex]\r\n\r\n37. a. [latex]f\\left(5\\right)=10[\/latex]; b. [latex]x=-1\\text{ }[\/latex] or [latex]\\text{ }x=4[\/latex]\r\n\r\n39. a. [latex]f\\left(t\\right)=6-\\frac{2}{3}t[\/latex]; b. [latex]f\\left(-3\\right)=8[\/latex]; c. [latex]t=6[\/latex]\r\n\r\n41. not a function\r\n\r\n43. function\r\n\r\n45. function\r\n\r\n47. function\r\n\r\n49. function\r\n\r\n51. function\r\n\r\n53. a. [latex]f\\left(0\\right)=1[\/latex]; b. [latex]f\\left(x\\right)=-3,x=-2\\text{ }[\/latex] or [latex]\\text{ }x=2[\/latex]\r\n\r\n55. not a function so it is also not a one-to-one function\r\n\r\n57. one-to-one function\r\n\r\n59. function, but not one-to-one\r\n\r\n61. function\r\n\r\n63. function\r\n\r\n65. not a function\r\n\r\n67. [latex]f\\left(x\\right)=1,x=2[\/latex]\r\n\r\n69. [latex]f\\left(-2\\right)=14\\\\ f\\left(-1\\right)=11\\\\ f\\left(0\\right)=8\\\\f\\left(1\\right)=5\\\\ f\\left(2\\right)=2[\/latex]\r\n\r\n71. [latex]f\\left(-2\\right)=4\\\\\\text{ }\\\\ f\\left(-1\\right)=4.414\\\\ f\\left(0\\right)=4.732\\\\ f\\left(1\\right)=4.5\\\\ f\\left(2\\right)=5.236[\/latex]\r\n\r\n73. [latex]f\\left(-2\\right)=\\frac{1}{9}\\\\ f\\left(-1\\right)=\\frac{1}{3}\\\\ f\\left(0\\right)=1\\\\ f\\left(1\\right)=3;\\\\f\\left(2\\right)=9[\/latex]\r\n\r\n75. 20\r\n\r\n77.\u00a0a. [latex]g\\left(5000\\right)=50[\/latex]; b. The number of cubic yards of dirt required for a garden of 100 square feet is 1.\r\n\r\n79. a. The height of a rocket above ground after 1 second is 200 ft. b. the height of a rocket above ground after 2 seconds is 350 ft.","rendered":"

Solutions to Odd-Numbered Exercises<\/span><\/h2>\n

1. A relation is a set of ordered pairs. A function is a special kind of relation in which no two ordered pairs have the same first coordinate.<\/p>\n

3. When a vertical line intersects the graph of a relation more than once, that indicates that for that input there is more than one output. At any particular input value, there can be only one output if the relation is to be a function.<\/p>\n

5. When a horizontal line intersects the graph of a function more than once, that indicates that for that output there is more than one input. A function is one-to-one if each output corresponds to only one input.<\/p>\n

7. function<\/p>\n

9. function<\/p>\n

11. function<\/p>\n

13. function<\/p>\n

15. function<\/p>\n

17. function<\/p>\n

19. function<\/p>\n

21. function<\/p>\n

23. function<\/p>\n

25. not a function<\/p>\n

27. [latex]f\\left(-3\\right)=-11\\\\ f\\left(2\\right)=-1\\\\ f\\left(-a\\right)=-2a - 5\\\\-f\\left(a\\right)=-2a+5\\\\f\\left(a+h\\right)=2a+2h - 5[\/latex]<\/p>\n

29. [latex]f\\left(-3\\right)=\\sqrt{5}+5\\\\ f\\left(2\\right)=5\\\\ f\\left(-a\\right)=\\sqrt{2+a}+5\\\\ -f\\left(a\\right)=-\\sqrt{2-a}-5\\\\f\\left(a+h\\right)=\\\\sqrt{2-a-h}+5[\/latex]<\/p>\n

31. [latex]f\\left(-3\\right)=2\\\\f\\left(2\\right)=1 - 3=-2\\\\f\\left(-a\\right)=|-a - 1|-|-a+1|\\\\ -f\\left(a\\right)=-|a - 1|+|a+1|\\\\\\text{ }\\text{ }f\\left(a+h\\right)=|a+h - 1|-|a+h+1|[\/latex]<\/p>\n

33. [latex]\\frac{g\\left(x\\right)-g\\left(a\\right)}{x-a}=x+a+2,x\\ne a[\/latex]<\/p>\n

35. a. [latex]f\\left(-2\\right)=14[\/latex]; b. [latex]x=3[\/latex]<\/p>\n

37. a. [latex]f\\left(5\\right)=10[\/latex]; b. [latex]x=-1\\text{ }[\/latex] or [latex]\\text{ }x=4[\/latex]<\/p>\n

39. a. [latex]f\\left(t\\right)=6-\\frac{2}{3}t[\/latex]; b. [latex]f\\left(-3\\right)=8[\/latex]; c. [latex]t=6[\/latex]<\/p>\n

41. not a function<\/p>\n

43. function<\/p>\n

45. function<\/p>\n

47. function<\/p>\n

49. function<\/p>\n

51. function<\/p>\n

53. a. [latex]f\\left(0\\right)=1[\/latex]; b. [latex]f\\left(x\\right)=-3,x=-2\\text{ }[\/latex] or [latex]\\text{ }x=2[\/latex]<\/p>\n

55. not a function so it is also not a one-to-one function<\/p>\n

57. one-to-one function<\/p>\n

59. function, but not one-to-one<\/p>\n

61. function<\/p>\n

63. function<\/p>\n

65. not a function<\/p>\n

67. [latex]f\\left(x\\right)=1,x=2[\/latex]<\/p>\n

69. [latex]f\\left(-2\\right)=14\\\\ f\\left(-1\\right)=11\\\\ f\\left(0\\right)=8\\\\f\\left(1\\right)=5\\\\ f\\left(2\\right)=2[\/latex]<\/p>\n

71. [latex]f\\left(-2\\right)=4\\\\\\text{ }\\\\ f\\left(-1\\right)=4.414\\\\ f\\left(0\\right)=4.732\\\\ f\\left(1\\right)=4.5\\\\ f\\left(2\\right)=5.236[\/latex]<\/p>\n

73. [latex]f\\left(-2\\right)=\\frac{1}{9}\\\\ f\\left(-1\\right)=\\frac{1}{3}\\\\ f\\left(0\\right)=1\\\\ f\\left(1\\right)=3;\\\\f\\left(2\\right)=9[\/latex]<\/p>\n

75. 20<\/p>\n

77.\u00a0a. [latex]g\\left(5000\\right)=50[\/latex]; b. The number of cubic yards of dirt required for a garden of 100 square feet is 1.<\/p>\n

79. a. The height of a rocket above ground after 1 second is 200 ft. b. the height of a rocket above ground after 2 seconds is 350 ft.<\/p>\n\n\t\t\t

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