1 00:00:00,000 --> 00:00:00,830 2 00:00:00,830 --> 00:00:03,160 We're asked to look at the table below. 3 00:00:03,160 --> 00:00:06,530 From the information given, is there a functional 4 00:00:06,530 --> 00:00:14,250 relationship between each person and his or her height? 5 00:00:14,250 --> 00:00:16,050 So a good place to start is just think about what a 6 00:00:16,050 --> 00:00:17,890 functional relationship means. 7 00:00:17,890 --> 00:00:19,429 Now, there's definitely a relationship. 8 00:00:19,429 --> 00:00:21,739 They say, hey, if you're Joelle, you're 5-6. 9 00:00:21,739 --> 00:00:23,449 If you're Nathan, you're 4-11. 10 00:00:23,449 --> 00:00:25,000 If you're Stewart, you're 5-11. 11 00:00:25,000 --> 00:00:26,989 That is a relationship. 12 00:00:26,989 --> 00:00:31,049 Now, in order for it to be a functional relationship, for 13 00:00:31,050 --> 00:00:34,820 every instance or every example of the independent 14 00:00:34,820 --> 00:00:38,000 variable, you can only have one example of the value of 15 00:00:38,000 --> 00:00:39,390 the function for it. 16 00:00:39,390 --> 00:00:48,730 So if you say if this is a height function, in order for 17 00:00:48,729 --> 00:00:52,609 this to be a functional relationship, no matter whose 18 00:00:52,609 --> 00:00:55,609 name you put inside of the height function, you need to 19 00:00:55,609 --> 00:00:58,049 only be able to get one value. 20 00:00:58,049 --> 00:01:01,019 If there were two values associated with one person's 21 00:01:01,020 --> 00:01:04,040 name, it would not be a functional relationship. 22 00:01:04,040 --> 00:01:08,915 So if I were to ask you what is the height of Nathan? 23 00:01:08,915 --> 00:01:12,680 24 00:01:12,680 --> 00:01:14,870 Well, you'd look at the table and say, well, Nathan's height 25 00:01:14,870 --> 00:01:19,910 is 4 foot 11. 26 00:01:19,909 --> 00:01:22,349 There are not two heights for Nathan. 27 00:01:22,349 --> 00:01:23,809 There is only one height. 28 00:01:23,810 --> 00:01:26,790 And for any one of these people that we can input into 29 00:01:26,790 --> 00:01:29,760 the function, there's only one height associated with them, 30 00:01:29,760 --> 00:01:31,660 so it is a functional relationship. 31 00:01:31,659 --> 00:01:33,879 We can even see that on a graph. 32 00:01:33,879 --> 00:01:35,289 Let me graph that out for you. 33 00:01:35,290 --> 00:01:38,859 34 00:01:38,859 --> 00:01:41,340 Let's see, the highest height here is 6 foot 1. 35 00:01:41,340 --> 00:01:49,370 So if we start off with one foot, two feet, three feet, 36 00:01:49,370 --> 00:01:57,329 four feet, five feet, and six feet. 37 00:01:57,329 --> 00:01:59,679 And then if I were to plot the different names, the different 38 00:01:59,680 --> 00:02:04,600 people that I could put into our height function, we have-- 39 00:02:04,599 --> 00:02:06,579 I'll just put the first letters of their names. 40 00:02:06,579 --> 00:02:12,990 We have Joelle, we have Nathan, we have Stewart, we 41 00:02:12,990 --> 00:02:17,540 have LJ, and then we have Tariq right there. 42 00:02:17,539 --> 00:02:19,090 So lets plot them. 43 00:02:19,090 --> 00:02:24,539 So you have Joelle, Joelle's height is 5-6, so 5-6 is right 44 00:02:24,539 --> 00:02:26,429 about there. 45 00:02:26,430 --> 00:02:29,800 Then you have Nathan. 46 00:02:29,800 --> 00:02:31,860 Let me do it in a different color. 47 00:02:31,860 --> 00:02:37,390 Nathan's height is 4-11. 48 00:02:37,389 --> 00:02:41,219 We will plot to him right over there. 49 00:02:41,219 --> 00:02:42,729 Then you have Stewart. 50 00:02:42,729 --> 00:02:47,009 Stewart's height is 5-11. 51 00:02:47,009 --> 00:02:48,909 He is pretty close to six feet. 52 00:02:48,909 --> 00:02:51,430 So Stewart's height-- I made him like six feet; let me make 53 00:02:51,430 --> 00:02:53,629 it a little lower-- is 5-11. 54 00:02:53,629 --> 00:02:57,060 Then you have LJ. 55 00:02:57,060 --> 00:02:59,560 LJ's height is 5-6. 56 00:02:59,560 --> 00:03:02,340 So you have two people with a height of 5-6, but that's OK, 57 00:03:02,340 --> 00:03:05,090 as long as for each person you only have one height. 58 00:03:05,090 --> 00:03:07,950 And then finally, Tariq is 6 foot 1. 59 00:03:07,949 --> 00:03:09,375 He's the tallest guy here. 60 00:03:09,375 --> 00:03:13,039 Tariq is right up here at 6 foot 1. 61 00:03:13,039 --> 00:03:16,599 So notice, for any one of the inputs into our function, we 62 00:03:16,599 --> 00:03:20,810 only have one value, so this is a functional relationship. 63 00:03:20,810 --> 00:03:23,694 Now, you might say OK, well, isn't everything a functional 64 00:03:23,694 --> 00:03:24,180 relationship? 65 00:03:24,180 --> 00:03:24,620 No! 66 00:03:24,620 --> 00:03:27,530 If I gave you the situation, if I also wrote here-- let's 67 00:03:27,530 --> 00:03:36,030 say the table was like this and I also wrote that Stewart 68 00:03:36,030 --> 00:03:37,759 is 5 foot 3 inches. 69 00:03:37,759 --> 00:03:40,560 If this was our table, then we would no longer have a 70 00:03:40,560 --> 00:03:43,949 functional relationship because for the input of 71 00:03:43,949 --> 00:03:46,129 Stewart, we would have two different values. 72 00:03:46,129 --> 00:03:49,979 If we were to graph this, we have Stewart here at 5-11, and 73 00:03:49,979 --> 00:03:52,979 then all of a sudden, we would also have Stewart at 5-3. 74 00:03:52,979 --> 00:03:55,299 Now, this doesn't make a lot of sense, so we would plot it 75 00:03:55,300 --> 00:03:56,510 right over here. 76 00:03:56,509 --> 00:03:59,049 So for Stewart, you would have two values, and so this 77 00:03:59,050 --> 00:04:02,880 wouldn't be a valid functional relationship because you 78 00:04:02,879 --> 00:04:06,210 wouldn't know what value to give if you were to take the 79 00:04:06,210 --> 00:04:10,120 height of Stewart. 80 00:04:10,120 --> 00:04:11,599 In order for this to be a function, there can only be 81 00:04:11,599 --> 00:04:12,889 one value for this. 82 00:04:12,889 --> 00:04:14,959 You don't know in this situation when I add this, 83 00:04:14,960 --> 00:04:17,240 whether it's 5-3 or 5-11. 84 00:04:17,240 --> 00:04:20,620 Now, this wasn't the case, so that isn't there and so we 85 00:04:20,620 --> 00:04:24,810 know that the height of Stewart is 5-11 and this is a 86 00:04:24,810 --> 00:04:26,300 functional relationship. 87 00:04:26,300 --> 00:04:29,220 I think to some level, it might be confusing, because 88 00:04:29,220 --> 00:04:30,800 it's such a simple idea. 89 00:04:30,800 --> 00:04:33,520 Each of these values can only have one height 90 00:04:33,519 --> 00:04:34,529 associated with it. 91 00:04:34,529 --> 00:04:35,599 That's what makes it a function. 92 00:04:35,600 --> 00:04:37,430 If you had more than one height associated with it, it 93 00:04:37,430 --> 00:04:39,449 would not be a function. 94 00:04:39,449 --> 00:04:39,865