More Math! Featuring Jean Miles

Shrimpeh: So, here we are Jean, and we're going to be learning how to Translate, reflect and scale parent funtions! yaaaay!

Jean: Oh shut up. You just recruited me because I lived in the freaking math district.

Shrimpeh: ... And your point is?

Jean: That I don't want to help you?

Shrimpeh: I made you, and I can just as easily smack you into oblivion.

Jean: no you wouldn't, you still want to do VP Uprising Posts

Shrimpeh: Shush.

Alright, so as you can clearly see, Shrimpeh needs to study this crap. I'll start now, I guess. This is merely child's play.

Reflections

Reflections is basically when you look in the mirror, and see the opposite image. Reflections normally occur in the x and y axis, but can occcur when y = k, or x = k. For example:

ry-axis
rx-axis
ry=3
rx=-3

When you have a parent function, and must find the equation after a reflection you do the following:

When the reflection is ry-axis, replace x with -x.
When the reflection is rx-axis, replace y with -y.
When the reflection is rx=k, replace x with 2k - x.
When the reflection is ry=k, replace y with 2k - y.

Make sure to put the replaced variable in parentheses.

ex: y = x² → rx=-3 → y = (-6 - x)²

Translations

Translations is when you move points (in this case, parent functions). Examples are

T_0,1
T_525600,1
T_-12,1/2

When you have a parent function, and must translate it, do the following.

T_a,b = replace:
y with y-b, and
x with x-a


y = 1/x² → T_2,-4

y + 4 = 1/(x - 2)²
y = 1/(x - 2)² + 4

Remember to always solve for y.