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Translations and Functions 1282 Views


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Description:

Translations: now without the trans fat. Functions: now without the…fun? Wait, scratch that. Now with extra fun! Don’t believe us? There's only one way to find out.

Language:
English Language

Transcript

00:07

Translations and Functions, a la Shmoop. In algebra, “translation” has nothing

00:12

to do with understanding a foreign language. Unless you consider algebra a foreign language..

00:17

Instead, it is about changing positions… like most politicians.

00:22

Those guys go up, down, backwards, forwards and side to side…

00:24

…wherever they need to go – and whatever they need to say - to make the voters happy.

00:29

But no matter how much shifting they may do… …they basically remain the same people.

00:33

Even if their integrity has taken a bit of a hit.

00:36

Same with the translation of shapes and curves on a coordinate plane.

00:39

You can scooch, slide and shove a shape in whatever direction you like…

00:43

…but as long as you don’t do anything drastic…

00:45

…it’s still going to be the same good ol’ shape you’ve grown to know and love.

00:48

So… how do you translate in terms of a function? In other words, how does a function affect

00:53

where a shape ends up on the plane? Let’s say we have the function f of x equals

00:59

5x. What does f of x plus seven look like?

01:03

Assuming you’re not catching it first thing in the morning, of course.

01:06

Well, the shape of its graph is exactly the same…

01:08

…except that it’s gone a-wanderin’. In this case… 7 units northward.

01:13

Good to see the little fella moving up in the world.

01:17

f (x) – 4? Same story, but now it gets shifted down 4 units.

01:22

Uh-oh. Looks like someone’s been banished to the dungeon.

01:25

Notice that, no matter how many times our trusty triangle changes its location…

01:29

…its dimensions and shape remain intact. Sorta like those… morally flexible politicians.

01:35

Not counting those who really let themselves go after an election.

01:37

YouTube blurb:

01:37

Translations – now without the trans fat. And functions – now without the… fun.

01:37

Wait, scratch that… now with extra fun! Don’t believe us? Only one way to find out…

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