WEBVTT 00:00:00.500 --> 00:00:05.815 - [Voiceover] "f is a finite function whose domain is the letters a to e. 00:00:05.815 --> 00:00:10.298 The following table lists the output for each input in f's domain." 00:00:10.298 --> 00:00:12.077 So if x is equal to a 00:00:12.077 --> 00:00:14.689 then, so if we input a into our function 00:00:14.689 --> 00:00:16.402 then we output -6. 00:00:16.402 --> 00:00:17.919 f of a is -6. 00:00:17.919 --> 00:00:20.445 We input b we get three, we input c we get -6, 00:00:20.445 --> 00:00:24.542 we input d we get two, we input e we get -6. 00:00:24.542 --> 00:00:28.832 "Build the mapping diagram for f by dragging the endpoints of the segments 00:00:28.832 --> 00:00:31.858 in the graph below so that they pair each domain element 00:00:31.858 --> 00:00:36.078 with its correct range element. Then, determine if f is invertible." 00:00:36.078 --> 00:00:38.716 Alright, so let's see what's going on over here. 00:00:38.716 --> 00:00:40.548 Let me scroll down a little bit more. 00:00:40.548 --> 00:00:44.501 So in this purple oval, this is representing the domain 00:00:44.501 --> 00:00:46.570 of our function f and this is the range. 00:00:46.570 --> 00:00:47.962 So the function is going to, 00:00:47.962 --> 00:00:49.798 if you give it a member of the domain 00:00:49.798 --> 00:00:51.879 it's going to map from that member of domain 00:00:51.879 --> 00:00:53.291 to a member of the range. 00:00:53.291 --> 00:00:56.681 So, for example, you input a into the function 00:00:56.681 --> 00:00:58.283 it goes to -6. 00:00:58.283 --> 00:01:01.718 So a goes to -6, so I drag that right over there. 00:01:01.718 --> 00:01:07.247 b goes to three, 00:01:07.247 --> 00:01:09.645 c goes to -6, so it's already interesting 00:01:09.645 --> 00:01:12.896 that we have multiple values that point to -6. 00:01:12.896 --> 00:01:15.464 So this is okay for f to be a function 00:01:15.464 --> 00:01:17.805 but we'll see it might make it a little bit tricky 00:01:17.805 --> 00:01:19.427 for f to be invertible. 00:01:19.427 --> 00:01:23.660 So let's see, d is points to two, or maps to two. 00:01:23.660 --> 00:01:26.949 So you input d into our function you're going to output two 00:01:26.949 --> 00:01:31.048 and then finally e maps to -6 as well. 00:01:31.048 --> 00:01:33.536 e maps to -6 as well. 00:01:33.536 --> 00:01:36.866 So, that's a visualization of how this function f maps 00:01:36.866 --> 00:01:40.208 from a through e to members of the range 00:01:40.208 --> 00:01:43.327 but also ask ourselves 'is this function invertible?' 00:01:43.327 --> 00:01:45.274 And I already hinted at it a little bit. 00:01:45.274 --> 00:01:48.985 Well in order fo it to be invertible you need a, 00:01:48.985 --> 00:01:51.946 you need a function that could take 00:01:51.946 --> 00:01:54.188 go from each of these points to, 00:01:54.188 --> 00:01:56.581 they can do the inverse mapping. 00:01:56.581 --> 00:01:58.567 But it has to be a function. 00:01:58.567 --> 00:02:01.786 So, if you input three into this inverse function 00:02:01.786 --> 00:02:03.074 it should give you b. 00:02:03.074 --> 00:02:05.472 If you input two into this inverse function 00:02:05.472 --> 00:02:07.814 it should output d. 00:02:07.814 --> 00:02:12.232 If you input -6 into this inverse function, 00:02:12.232 --> 00:02:14.909 well this hypothetical inverse function. 00:02:14.909 --> 00:02:16.488 what should it do? 00:02:16.488 --> 00:02:18.992 Well you can't have a function that if you input one, 00:02:18.992 --> 00:02:22.623 if you input a number it could have three possible values, 00:02:22.623 --> 00:02:26.575 a, c, or e, you can only map to one value. 00:02:26.575 --> 00:02:28.540 So there isn't, you actually can't set up 00:02:28.540 --> 00:02:30.173 an inverse function that does this 00:02:30.203 --> 00:02:31.825 because it wouldn't be a function. 00:02:31.825 --> 00:02:34.297 You can't go from input -6 into that inverse function 00:02:34.297 --> 00:02:36.050 and get three different values. 00:02:36.050 --> 00:02:38.845 So this is not invertible. 00:02:38.845 --> 00:02:41.188 Let's do another example. 00:02:41.188 --> 00:02:43.990 So here, so this is the same drill. 00:02:43.990 --> 00:02:46.717 We have our members of our domain, members of our range. 00:02:46.717 --> 00:02:48.664 We can build our mapping diagram. 00:02:48.664 --> 00:02:51.390 a maps to -36, 00:02:51.390 --> 00:02:53.946 b maps to nine. 00:02:53.946 --> 00:02:57.735 c maps to -4, 00:02:57.735 --> 00:03:00.498 d maps to 49, 00:03:00.498 --> 00:03:04.990 and then finally e maps to 25. 00:03:04.990 --> 00:03:08.321 e maps to 25. 00:03:08.321 --> 00:03:11.245 Now is this function invertible? 00:03:11.245 --> 00:03:12.510 Well let's think about it. 00:03:12.510 --> 00:03:15.725 The inverse, woops, the, was it d maps to 49 00:03:15.725 --> 00:03:17.589 So, let's think about what the inverse, 00:03:17.589 --> 00:03:20.017 this hypothetical inverse function would have to do. 00:03:20.017 --> 00:03:22.637 It would have to take each of these members of the range 00:03:22.637 --> 00:03:23.931 and do the inverse mapping. 00:03:23.931 --> 00:03:27.419 So if you input 49 into our inverse function 00:03:27.419 --> 00:03:28.495 it should give you d. 00:03:28.495 --> 00:03:30.356 Input 25 it should give you e. 00:03:30.356 --> 00:03:32.393 Input nine it gives you b. 00:03:32.393 --> 00:03:34.618 You input -4 it inputs c. 00:03:34.618 --> 00:03:37.353 You input -36 it gives you a. 00:03:37.353 --> 00:03:40.794 So you could easily construct an inverse function here. 00:03:40.794 --> 00:03:45.216 So this is very much, this is very much invertible. 00:03:45.216 --> 00:03:47.780 One way to think about it is these are a, 00:03:47.780 --> 00:03:51.404 this is a one to one mapping. 00:03:51.404 --> 00:03:53.679 Each of the members of the domain 00:03:53.679 --> 00:03:55.989 correspond to a unique member of the range. 00:03:55.989 --> 00:03:57.952 You don't have two members of the domain 00:03:57.952 --> 00:04:00.953 pointing to the same member of the range. 00:04:00.953 --> 00:04:03.142 Anyway, hopefully you found that interesting.