1
00:00:00,000 --> 00:00:00,670


2
00:00:00,670 --> 00:00:03,980
We are asked to represent the following function on the

3
00:00:03,980 --> 00:00:04,820
coordinate plane.

4
00:00:04,820 --> 00:00:08,560
And they give us domain, and then they give us a range, a

5
00:00:08,560 --> 00:00:11,250
set of values that our function can take on.

6
00:00:11,250 --> 00:00:13,970
And the way the question has been phrased, I'm assuming

7
00:00:13,970 --> 00:00:19,820
they assume that the negative 8 maps to the 4, the negative

8
00:00:19,820 --> 00:00:24,260
6 maps to the 3, the negative 4 maps to the 2, the negative

9
00:00:24,260 --> 00:00:27,310
2 maps to 1, and the 0 maps to 0.

10
00:00:27,309 --> 00:00:30,119
Because you could have another function with this exact same

11
00:00:30,120 --> 00:00:33,090
domain, and this exact same range, where the mapping is

12
00:00:33,090 --> 00:00:35,480
different, where negative 8 maps to 3, and

13
00:00:35,479 --> 00:00:36,889
negative 6 maps to 4.

14
00:00:36,890 --> 00:00:39,649
So this domain and this range could be for

15
00:00:39,649 --> 00:00:40,879
many different functions.

16
00:00:40,880 --> 00:00:44,070
But when they say represent the following function, I'm

17
00:00:44,070 --> 00:00:47,469
assuming that they want us to assume that they're kind of in

18
00:00:47,469 --> 00:00:48,689
order, the pairing.

19
00:00:48,689 --> 00:00:51,599
So let's just graph this function, or represent it

20
00:00:51,600 --> 00:00:53,450
using their terminology.

21
00:00:53,450 --> 00:00:56,130
So let me draw some axes here.

22
00:00:56,130 --> 00:01:00,200
So this is the domain, the independent variable, just

23
00:01:00,200 --> 00:01:04,719
like that, often known as the x-axis or the horizontal axis.

24
00:01:04,719 --> 00:01:07,250
And all of our domain, all of the values, these are all

25
00:01:07,250 --> 00:01:10,790
non-positive numbers, so let me give a lot more space to

26
00:01:10,790 --> 00:01:11,320
quadrant II.

27
00:01:11,319 --> 00:01:12,979
All of our range are positive numbers.

28
00:01:12,980 --> 00:01:15,939
They're going to be hanging out in the top left quadrant,

29
00:01:15,939 --> 00:01:19,670
or quadrant II, just like that.

30
00:01:19,670 --> 00:01:23,100
And the values that my domain can take on are 0 through

31
00:01:23,099 --> 00:01:26,780
negative 8, and every even negative number.

32
00:01:26,780 --> 00:01:31,260
So it's 0, let me do it like this, so 0 is there.

33
00:01:31,260 --> 00:01:38,340
And then we have negative 2, negative 4, negative 6, and

34
00:01:38,340 --> 00:01:42,159
then we have negative 8 just like that.

35
00:01:42,159 --> 00:01:44,920
And then our range goes from 0 through 4.

36
00:01:44,920 --> 00:01:49,960
So this is 0, then you have 1, then you have 2, then you have

37
00:01:49,959 --> 00:01:52,559
3, and then you have 4.

38
00:01:52,560 --> 00:01:55,870
So if we assume the mapping, that if you give this function

39
00:01:55,870 --> 00:01:58,609
a negative 8, it's going to map to 4, then

40
00:01:58,609 --> 00:01:59,590
we can plot it here.

41
00:01:59,590 --> 00:02:03,170
So if we take this first pair right there, you give me a

42
00:02:03,170 --> 00:02:05,489
negative 8, this function is going to give me a 4.

43
00:02:05,489 --> 00:02:09,538
So negative 8, 4 is that point right there.

44
00:02:09,538 --> 00:02:12,389
So if you imagine that this is the x-axis, this would be the

45
00:02:12,389 --> 00:02:16,699
f of x axis, if we're assuming that f is this function.

46
00:02:16,699 --> 00:02:22,319
You give me a negative 6, I'll give you a 3.

47
00:02:22,319 --> 00:02:25,539
Negative 6 and 3.

48
00:02:25,539 --> 00:02:31,739
You give me a negative 4, this function will pop out a 2.

49
00:02:31,740 --> 00:02:34,640
Negative 4 comma 2.

50
00:02:34,639 --> 00:02:38,039
And then you give a negative 2, this function

51
00:02:38,039 --> 00:02:39,060
will pop out a 1.

52
00:02:39,060 --> 00:02:40,909
F of negative 2 is 1.

53
00:02:40,909 --> 00:02:44,090


54
00:02:44,090 --> 00:02:48,030
And then finally, f of 0 is 0.

55
00:02:48,030 --> 00:02:50,890
So we'll just plot it right there.

56
00:02:50,889 --> 00:02:51,799
So that's the function.

57
00:02:51,800 --> 00:02:52,930
I've represented it.

58
00:02:52,930 --> 00:02:56,710
And remember, I just assumed that negative 8 maps to 4,

59
00:02:56,710 --> 00:02:59,879
negative 6 maps to 3, but you could have multiple functions

60
00:02:59,879 --> 00:03:01,609
that have this domain and range.

61
00:03:01,610 --> 00:03:03,950
But just the way that they said the following function,

62
00:03:03,949 --> 00:03:07,439
I'm assuming this is what they want us to do.

63
00:03:07,439 --> 00:03:07,466