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Functions Videos 43 videos
Don’t even think about starting up your combo lemonade/fro-yo stand without first making sure you understand piecewise functions. You’re just a...
Domain and range: two terms you will learn to love (or hate with a vengeance). The domain is the set of all possible x values, and range is the set...
Functions briefly flirted with the idea of being infomercial hosts, but they didn’t shine when talking on-camera. They’re much better off in th...
Translations and Functions 1284 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.
- Mathematics and Statistics Assessment / Transformations and Symmetry
- Geometry / Experiment with transformations in the plane
- Geometry / Understand congruence in terms of rigid motions
- Geometry / Understand similarity in terms of similarity transformations
- Congruence / Experiment with transformations in the plane
- Congruence / Understand congruence in terms of rigid motion
- Similarity, Right Triangles, and Trigonometry / Understand similarity in terms of transformations
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.
Full Transcript
- 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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