## Transformations

Quadratic equations and inequalities, variation equations, function notation, systems of equations, etc.
hakandragon
Posts: 13
Joined: Mon May 04, 2009 10:08 pm
Contact:

### Transformations

Hi everyone, I couldn't tell where to put this, so I thought here would be best, I hope that's ok.

Anyways, I don't really have a question like all the others, more just topic based. How On Earth Do I Do Math Transformations?!?!? My book is useless! It gives me a load of diagrams and numbers, and expects me to understand it all and how it's done! Well I don't, I can't! Is there not some simple formula I can follow? I'm not good at math people, I don't want to be a rocket scientist! It doesn't help that I'm mildly dyslexic, and I have mega trouble remembering things!

I'm sorry, I know I got off topic/ranty there, but I just get so upset about it all. I'm a writer, not a human-calculator. I don't do these sorts of things.

Anyways. Transformations. I get the idea of them, that it's just something being moved down or right a certain number of spaces, but HOW is it done? I'm given something like "Use the sketch of f(x) to sketch each function ***Diagram***" and then a whole bunch of f(x)+5, f(-2)x, 1/(f(x)), etc etc. What do I do with those? How do I figure all this out?

Please help if you can, I really am trying hard to understand things. Thank you so much.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
See if this lesson is helpful at all....

hakandragon
Posts: 13
Joined: Mon May 04, 2009 10:08 pm
Contact:

### Re: Transformations

f(x) + a is f(x) shifted upward a units
f(x) – a is f(x) shifted downward a units
f(x + a) is f(x) shifted left a units
f(x – a) is f(x) shifted right a units
–f(x) is f(x) flipped upside down ("reflected about the x-axis")
f(–x) is the mirror of f(x) ("reflected about the y-axis")
Where can I find a larger list of these? Or is this all of them o_O

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
Contact:
The other two transformations (often not covered until trigonometry) are scaling:

. . . . .f(ax): f(x), but stretched "a" times wider (if |a| < 1)
. . . . . . . . ..or squished to only "a" times as wide (if |a| > 1)

...and amplitude:

. . . . .a*f(x): f(x), but streched "a" times taller (if |a| > 1)
. . . . . . . . . .or squished only "a" times as tall (if |a| < 1)