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[Dino and Coop singing]

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We know a thing or two about how functions capture patterns…

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Y'know, like how the pattern 4, 7, 10, 13… [Woman points to a blackboard]

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…can be summed up with the function 3x + 1.

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But what if we told you that these functions also have a very visual side?

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And no, not like "Michael Bay robot explosion movies" visual, but maybe that's for the best. [Robot explodes on a theater screen]

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Let's say we have a pattern summed up by the function x + 3.

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We can show this pattern in a table, where for each value of x, we see what value of

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y the function spits out.

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For example, since 0 + 3 = 3…

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…our first y value will be 3. [The value is written into the table]

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And if we take 1, 2, and 3, and stick each of them into our function…

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…we find the rest of our y values. [The table is completed]

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Man, y didn't we learn about this earlier??

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…Get it?

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It's a joke, because….y sounds like…

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Oooookay...

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Moving on.

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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]

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functions get even more visual. [Student offers to do interpretive dance to make the class more interesting]

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That's because this table can be translated into the Cartesian coordinate plane.

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It has a horizontal axis, which represents x values…

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…and a vertical axis, which represents y values.

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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]

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number shows where the point is relative to the x-axis…like so…

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…and the second number shows where the point is relative to the y-axis.

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These ordered pairs are kinda like secret treasure maps. [A treasure map is lowered and a jungle revealed]

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Except if you follow them you find points, instead of gold coins. [Pirate next to a treasure chest]

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Hey, at least points aren't as heavy, right?

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It turns out we can think of each entry in our table as an ordered pair of coordinates.

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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]

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The same thinking gives us ordered pairs for the rest of the rows.

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And with all of these ordered pairs in hand, we can plot them on the plane.

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Let's start with (0, 3).

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Its x value is 0, so it'll be where x = 0 on the x-axis.

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Plus, its y value is 3, so it'll be where y = 3 on the y-axis. [The coordinate is plotted]

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And, surprise surprise, if we follow that exact same procedure, we can graph the rest

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of our points.

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If that's not enough excitement for you, you can even connect all of those points, to form [All of the coordinates are plotted]

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one line that represents our function. [A line is drawn between the coordinates]

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We know, seeing a straight line and a bunch of numbers is pretty exciting stuff.

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Please try to remain calm. [Student is dancing in a pink tutu]

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It'll be tough, but we bet you can…

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