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Math 5: In & Out Tables With Graphed Ordered Pairs 21 Views
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Description:
Did you know that there's a relationship between functions and patterns? Shhh, don't tell anyone. They're keeping it on the DL.
Transcript
- 00:02
[Dino and Coop singing]
- 00:13
We know a thing or two about how functions capture patterns…
- 00:17
Y'know, like how the pattern 4, 7, 10, 13… [Woman points to a blackboard]
- 00:19
…can be summed up with the function 3x + 1.
- 00:23
But what if we told you that these functions also have a very visual side?
Full Transcript
- 00:27
And no, not like "Michael Bay robot explosion movies" visual, but maybe that's for the best. [Robot explodes on a theater screen]
- 00:32
Let's say we have a pattern summed up by the function x + 3.
- 00:36
We can show this pattern in a table, where for each value of x, we see what value of
- 00:41
y the function spits out.
- 00:42
For example, since 0 + 3 = 3…
- 00:46
…our first y value will be 3. [The value is written into the table]
- 00:48
And if we take 1, 2, and 3, and stick each of them into our function…
- 00:52
…we find the rest of our y values. [The table is completed]
- 00:54
Man, y didn't we learn about this earlier??
- 00:57
…Get it?
- 00:58
It's a joke, because….y sounds like…
- 01:01
Oooookay...
- 01:02
Moving on.
- 01:03
If you're not exactly wowed by the appearance of a table full of numbers, don't worry: these [Kids asleep in class and one falls to the floor]
- 01:08
functions get even more visual. [Student offers to do interpretive dance to make the class more interesting]
- 01:10
That's because this table can be translated into the Cartesian coordinate plane.
- 01:15
It has a horizontal axis, which represents x values…
- 01:18
…and a vertical axis, which represents y values.
- 01:21
So any point on this plane can be represented by an ordered pair (x, y), where the first [A coordinate is plotted onto the axis]
- 01:25
number shows where the point is relative to the x-axis…like so…
- 01:29
…and the second number shows where the point is relative to the y-axis.
- 01:34
These ordered pairs are kinda like secret treasure maps. [A treasure map is lowered and a jungle revealed]
- 01:37
Except if you follow them you find points, instead of gold coins. [Pirate next to a treasure chest]
- 01:40
Hey, at least points aren't as heavy, right?
- 01:43
It turns out we can think of each entry in our table as an ordered pair of coordinates.
- 01:48
For example, that first row of entries is (0, 3), because x = 0, and y = 3. [The values from the table are written as coordinates]
- 01:53
The same thinking gives us ordered pairs for the rest of the rows.
- 01:57
And with all of these ordered pairs in hand, we can plot them on the plane.
- 02:00
Let's start with (0, 3).
- 02:02
Its x value is 0, so it'll be where x = 0 on the x-axis.
- 02:06
Plus, its y value is 3, so it'll be where y = 3 on the y-axis. [The coordinate is plotted]
- 02:11
And, surprise surprise, if we follow that exact same procedure, we can graph the rest
- 02:15
of our points.
- 02:17
If that's not enough excitement for you, you can even connect all of those points, to form [All of the coordinates are plotted]
- 02:21
one line that represents our function. [A line is drawn between the coordinates]
- 02:23
We know, seeing a straight line and a bunch of numbers is pretty exciting stuff.
- 02:27
Please try to remain calm. [Student is dancing in a pink tutu]
- 02:29
It'll be tough, but we bet you can…
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