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Ex: Function and Inverse Function Values Using a Graph — Transcript

by Mathispower4u · 774 words · 87 segments · language en · Watch on YouTube
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  1. 0:00- HERE WE'RE ASKED TO USE THE GRAPH OF FUNCTION F OF X
  2. 0:03GRAPHED HERE IN RED
  3. 0:04TO DETERMINE THE VALUES HERE ON THE RIGHT.
  4. 0:06NOTICE TWO OF THESE INVOLVE THE FUNCTION F
  5. 0:09AND TWO INVOLVE THE INVERSE OF FUNCTION F.
  6. 0:12TO EVALUATE F OF 2 WE NEED TO RECOGNIZE
  7. 0:14THAT THIS 2 IS THE INPUT OR THE X VALUE FOR FUNCTION F.
  8. 0:18SO LOOKING AT THE GRAPH OF FUNCTION F
  9. 0:20HERE'S THE X VALUE OF +2.
  10. 0:23SO IF WE GO UP TO THE FUNCTION WE CAN USE THIS POINT RIGHT HERE
  11. 0:29TO DETERMINE THE FUNCTION VALUE.
  12. 0:31NOTICE THE X COORDINATE IS 2 AND THE Y COORDINATE IS +4,
  13. 0:37WELL THE Y COORDINATE IS THE OUTPUT FOR THE FUNCTION
  14. 0:40WHEN X IS 2.
  15. 0:42THEREFORE, F OF 2 EQUALS 4.
  16. 0:44LET'S ALSO RECORD THIS INFORMATION IN THIS TABLE HERE
  17. 0:47FOR THE TABLE OF VALUES FOR F OF X.
  18. 0:50WHEN X = 2 THE OUTPUT OR FUNCTION VALUE IS 4.
  19. 0:56NEXT, WE'RE TOLD IF F OF X = 2 DETERMINE THE VALUE OF X.
  20. 1:01WELL HERE, 2 IS THE OUTPUT OR THE Y VALUE OF THE FUNCTION.
  21. 1:06SO GOING BACK OVER TO OUR GRAPH
  22. 1:07NOW WE WANT TO FIND WHERE THE Y COORDINATE = 2.
  23. 1:11WELL THE Y COORDINATE IS EQUAL TO 2 RIGHT HERE ON THE Y AXIS.
  24. 1:15THE COORDINATES OF THIS POINT WOULD BE (0, 2).
  25. 1:19SO WHEN THE FUNCTION VALUE OR Y VALUE IS +2
  26. 1:23THE X VALUE OR INPUT IS EQUAL TO ZERO.
  27. 1:26SO IF F OF X = 2 THAN X = 0.
  28. 1:29AGAIN, IF YOU WANT TO RECORD THIS INFORMATION
  29. 1:31IN A TABLE OF VALUES
  30. 1:32WE WOULD HAVE X = 0 AND Y OR THE FUNCTION VALUE IS = +2.
  31. 1:38NOW THE REASON I WANTED TO RECORD THIS INFORMATION
  32. 1:39IN A TABLE
  33. 1:41IS BECAUSE IF WE COMPLETE A TABLE OF VALUES
  34. 1:43FOR THE INVERSE FUNCTION
  35. 1:44IT WILL HELP US ANSWER THESE LAST TWO QUESTIONS
  36. 1:46INVOLVING THE INVERSE OF FUNCTION F.
  37. 1:49REMEMBER F AND F INVERSE UNDO EACH OTHER
  38. 1:52SO IF THE INPUT FOR FUNCTION F IS 2 AND THE OUTPUT IS 4
  39. 1:56THEN IF THE INPUT FOR THE INVERSE FUNCTION IS 4
  40. 1:59THEN THE OUTPUT WOULD BE EQUAL TO 2.
  41. 2:02IF THE INPUT FOR F IS ZERO AND THE OUTPUT IS 2
  42. 2:06THEN IF THE INPUT IS 2 FOR THE INVERSE FUNCTION
  43. 2:09THE OUTPUT WOULD BE ZERO.
  44. 2:11SO WE CAN SEE THESE TWO FUNCTIONS
  45. 2:12ARE UNDOING EACH OTHER.
  46. 2:14SO LOOKING AT THESE LAST TWO TO EVALUATE F INVERSE OF 2
  47. 2:18WE NEED TO RECOGNIZE THAT THIS 2 HERE
  48. 2:20IS THE INPUT INTO THE INVERSE FUNCTION
  49. 2:22AND WE WANT TO DETERMINE THE OUTPUT OR FUNCTION VALUE.
  50. 2:25SO LOOKING AT THIS TABLE OF VALUES FOR THE INVERSE FUNCTION
  51. 2:28NOTICE WHEN THE INPUT IS 2 OR X = 2 THE OUTPUT IS ZERO
  52. 2:33SO F INVERSE OF 2 = 0.
  53. 2:36IF WE WANTED TO FIND THIS VALUE USING THE GRAPH
  54. 2:38WE WOULD HAVE TO RECOGNIZE THAT FOR THE INVERSE FUNCTION
  55. 2:41THIS Y COORDINATE OR FUNCTION VALUE WOULD BE THE INPUT
  56. 2:45AND THE X COORDINATE OR ZERO WOULD ACTUALLY BE THE OUTPUT.
  57. 2:48AND THAT CAN BE A LITTLE TRICKY AT FIRST
  58. 2:50AND THAT'S WHY IT'S OFTEN HELPFUL
  59. 2:51TO RECORD THE INFORMATION ABOUT THE INVERSE FUNCTION
  60. 2:54IN A DIFFERENT TABLE.
  61. 2:56LOOKING AT THE LAST QUESTION, IF F INVERSE OF X = 2
  62. 3:00MEANING IF THE OUTPUT OF THE INVERSE FUNCTION IS EQUAL TO +2
  63. 3:04WE WANT TO DETERMINE THE X VALUE.
  64. 3:06SO AGAIN LOOKING AT OUR TABLE OF VALUES FOR THE INVERSE FUNCTION
  65. 3:08NOTICE IF THE OUTPUT FOR THE INVERSE FUNCTION IS 2
  66. 3:12THE INPUT OR X VALUE IS EQUAL TO +4.
  67. 3:16AGAIN LOOKING BACK AT THE GRAPH WE'D HAVE TO RECOGNIZE
  68. 3:18THAT IF F INVERSE OF X = 2
  69. 3:22THIS 2 HERE WOULD BE THE OUTPUT OF THE INVERSE FUNCTION
  70. 3:24AND THE INPUT WOULD EQUAL THIS 4 HERE.
  71. 3:27THERE IS ONE MORE IMPORTANT CONNECTION I'D LIKE TO MAKE.
  72. 3:29IF WE TAKE A LOOK AT THIS FIRST QUESTION AND THIS LAST QUESTION
  73. 3:34THERE IS A CONNECTION.
  74. 3:36NOTICE WHEN THE INPUT INTO THE FUNCTION F IS 2
  75. 3:39THE OUTPUT IS 4
  76. 3:42AND IF THE OUTPUT OF THE INVERSE FUNCTION IS 2
  77. 3:45THEN THE INPUT IS EQUAL TO 4.
  78. 3:47THIS INFORMATION HERE IS THE SAME INFORMATION
  79. 3:49WE HAVE HERE IN THIS FIRST ROW OF THESE TWO TABLES.
  80. 3:54AND THEN THIS QUESTION HERE AND THIS QUESTION HERE
  81. 3:57ARE ALSO RELATED.
  82. 3:59FOR FUNCTION F, IF THE OUTPUT IS 2, THE INPUT IS 0,
  83. 4:04AND FOR THE INVERSE FUNCTION IF THE INPUT IS 2 THE OUTPUT IS 0,
  84. 4:09THESE TWO QUESTIONS HERE
  85. 4:10EMPHASIS THE RELATIONSHIP BETWEEN THE FUNCTION F
  86. 4:13FROM THESE TWO ROWS HERE.
  87. 4:16I HOPE YOU FOUND THIS HELPFUL.

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