Ex: Determine the Least Possible Degree of a Polynomial From the Graph — Transcript

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1. 0:00- WELCOME TO TWO EXAMPLES OF DETERMINING
2. 0:03THE LEAST POSSIBLE DEGREE OF A POLYNOMIAL FUNCTION
3. 0:06FROM THE GRAPH OF THE FUNCTION.
4. 0:08THESE QUESTIONS EMPHASIZE WHAT THE DEGREE OF A FUNCTION TELL US
5. 0:11ABOUT THE GRAPH OF THE FUNCTION.
6. 0:13SO TO REVIEW, IF A POLYNOMIAL FUNCTION HAS DEGREE N,
7. 0:18THEN THE FUNCTION HAS AT MOST N X INTERCEPTS,
8. 0:22AND THE FUNCTION HAS AT MOST N - 1 TURNS.
9. 0:26LOOKING AT THE GRAPH OF OUR POLYNOMIAL FUNCTION,
10. 0:29NOTICE HOW IT HAS TWO X INTERCEPTS,
11. 0:31SO IT MUST BE AT LEAST A DEGREE TWO POLYNOMIAL FUNCTION,
12. 0:35BUT NOW LET'S TAKE A LOOK AT THE NUMBER OF TURNS
13. 0:36THE FUNCTION HAS.
14. 0:38THE FUNCTION HAS A TURN HERE, 1, A TURN HERE, THAT'S 2,
15. 0:43AND ALSO A TURN HERE.
16. 0:45SO IT HAS THREE TURNS.
17. 0:47WHEN A FUNCTION TURNS, WE HAVE A HIGH POINT OR A LOW POINT
18. 0:50ON THE GRAPH OF THE FUNCTION.
19. 0:52WE'LL THROW OUT MOST N - 1 TURNS, AND WE HAVE THREE TURNS,
20. 0:57THEN OUR DEGREE N MUST BE AT LEAST 4.
21. 1:01SO BY THE GRAPH OF THIS POLYNOMIAL FUNCTION,
22. 1:03WE KNOW THE LEAST POSSIBLE DEGREE
23. 1:05WOULD BE A FOURTH DEGREE POLYNOMIAL FUNCTION.
24. 1:09LET'S TAKE A LOOK AT A SECOND EXAMPLE.
25. 1:13AGAIN, OUR GRAPH HAS ONE X INTERCEPT,
26. 1:16SO THE GRAPH MUST BE AT LEAST A DEGREE 1,
27. 1:18BUT WE KNOW IT HAS TO BE HIGHER THAN THAT
28. 1:20BECAUSE A DEGREE 1 FUNCTION WOULD BE A LINE.
29. 1:23SO LET'S TAKE A LOOK AT THE NUMBER OF TURNS.
30. 1:25WELL, THIS POLYNOMIAL FUNCTION HAS 1, 2 TURNS,
31. 1:29AND, AGAIN, EACH POLYNOMIAL FUNCTION HAS AT MOST N - 1 TURNS
32. 1:34SO N THE DEGREE MUST BE AT LEAST 3 IF THIS FUNCTION HAS 2 TURNS.
33. 1:41SO THE LEAST POSSIBLE DEGREE FOR THIS POLYNOMIAL FUNCTION
34. 1:44WOULD BE A THIRD DEGREE POLYNOMIAL FUNCTION.