ShmoopTube

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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YouTube blurb:

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

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

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