1
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In the following graph, is y a function of x?

2
00:00:04,866 --> 00:00:08,472
So, in order for y to be a function of x,

3
00:00:08,472 --> 00:00:11,493
for any x that you input into the function,

4
00:00:11,493 --> 00:00:14,819
any x for which the function is defined –

5
00:00:15,450 --> 00:00:17,633
So let's say we have y is equal to f(x),

6
00:00:17,773 --> 00:00:19,588
So we have our little function machine.

7
00:00:19,588 --> 00:00:24,128
it should spit out exactly one value of y.

8
00:00:24,128 --> 00:00:26,238
If it spits out multiple values of y,

9
00:00:26,238 --> 00:00:28,632
we don't know what f(x) is going to be equal to.

10
00:00:28,632 --> 00:00:31,295
It could be equal to any of those possible values for y.

11
00:00:31,295 --> 00:00:35,215
So, let's see if, for this graph, whether, for a given x,

12
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it spits out exactly one y.

13
00:00:38,285 --> 00:00:41,549
Well, the function seems to be only defined –

14
00:00:41,549 --> 00:00:44,354
so the domain of this function is x is equal to -2.

15
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That's the only place where we have a definition for it.

16
00:00:46,416 --> 00:00:53,947
– and if we try to input -2 into this little black box,

17
00:00:53,947 --> 00:00:55,015
what do we get?

18
00:00:55,015 --> 00:00:57,090
Do we get exactly one thing?

19
00:00:57,090 --> 00:01:00,549
No. [If] we put -2 in here, we could get anything.

20
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The point -2, 9 is on this relation.

21
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-2, 8 is on this relation.

22
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-2, 7

23
00:01:07,649 --> 00:01:08,833
-2, 7.5

24
00:01:08,833 --> 00:01:10,901
-2, 3.14159

25
00:01:10,901 --> 00:01:12,363
They're all on these.

26
00:01:12,363 --> 00:01:16,172
So, if you put a negative 2 into this relation, you actually get –

27
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essentially, you actually get an infinite set of values.

28
00:01:19,765 --> 00:01:22,834
It could be 9. It could be 3.14.

29
00:01:22,834 --> 00:01:25,647
It could be 8. It could be -8.

30
00:01:25,647 --> 00:01:28,032
You get an infinite number of results.

31
00:01:28,032 --> 00:01:32,244
So, since it does not map to exactly one output of this function,

32
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in the following graph, y is NOT a function of x.