Translations and Functions
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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.
|Congruence||Experiment with transformations in the plane|
Understand congruence in terms of rigid motion
|Geometry||Experiment with transformations in the plane|
Understand congruence in terms of rigid motions
Understand similarity in terms of similarity transformations
|Mathematics and Statistics Assessment||Transformations and Symmetry|
|Similarity, Right Triangles, and Trigonometry||Understand similarity in terms of transformations|
But no matter how much shifting they may do… …they basically remain the same people.
Even if their integrity has taken a bit of a hit.
Same with the translation of shapes and curves on a coordinate plane.
You can scooch, slide and shove a shape in whatever direction you like…
…but as long as you don’t do anything drastic…
…it’s still going to be the same good ol’ shape you’ve grown to know and love.
So… how do you translate in terms of a function? In other words, how does a function affect
where a shape ends up on the plane? Let’s say we have the function f of x equals
5x. What does f of x plus seven look like?
Assuming you’re not catching it first thing in the morning, of course.
Well, the shape of its graph is exactly the same…
…except that it’s gone a-wanderin’. In this case… 7 units northward.
Good to see the little fella moving up in the world.
f (x) – 4? Same story, but now it gets shifted down 4 units.
Uh-oh. Looks like someone’s been banished to the dungeon.
Notice that, no matter how many times our trusty triangle changes its location…
…its dimensions and shape remain intact. Sorta like those… morally flexible politicians.
Not counting those who really let themselves go after an election.
Translations – now without the trans fat. And functions – now without the… fun.
Wait, scratch that… now with extra fun! Don’t believe us? Only one way to find out…