Putting It All Together

Hey guys, This is Angelo!
This blog is going to talk about how to put all the transformations, translations, reflections and stretching together. 

Let's start with the equation.

 "a" and "d" are both outside and must read as it is.

 "b" and "c" are both inside and must be read as opposites.

Now that you know the equation, let's work on some examples.

Given the following graph of f(x), graph the transformation "-f(x+1)-3".

This transformation formula has just about everything. There's a left-shift of one (the "+1" inside), a move-down by three (the "–3" outside), and a flip-upside-down (the "minus" sign out front). And, worse yet, I have no formula for f(x), so I can't cheat; I have to do the transformation.

Let's work on the first point (-3,-2).

I'll shift the point by 1 unit, making it (-4,-2).
Then I will flip the point over the x-axis making it (-4,2).
I will then move the point down 3 units to (-4,-1).

We're done 1 out of 4 points.
On to the next point.

I'll shift the point by 1 unit, making it (-3,-4).
Flip the point across the x-axis making it (-3,4) then making the point go down 3 units making it (-3,1).

2 points out of 4 done.
Repeat the steps for the next 2 points which I will skip for length purposes.

...And you should end up with this. 

This is pretty much how you do everything all at ones. I hope you enjoyed reading this and I hope it actually helped you out! I'm sorry I don't have much funny pictures to put on here, maybe next time I'd think of more clever way of putting pictures in. 


- Angelo signing out, Peace out A-Town.