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Math Videos 43 videos

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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.

Language:
English Language

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?

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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