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### GMC Forum _ CHILL OUT _ Precalculus Help

#### Posted by: FretDancer69 Oct 21 2007, 06:13 AM

Hey guys, i gotta make a booklet about Graphical Transformations and i have no idea what to do. My teacher sucks at "teaching" and i dont understand anything. Can someone help me please.

Here are the instructions:

GRAPHICAL TRANSFORMATIONS

Objective: To represent translations, reflections, stretches and shrinks of functions algebraically and graphically.

Graphical transformations:
• Vertical and horizontal translations
• reflections across the axes (odd and even functions)
• Vertical and horizontal stretches and shrinks
• Combining transformations
Parent functions to transform:

F(x) = x^n, n=2,3,1/2
F(x) = |x|
F(x) = [x]

_______________________

#### Posted by: Tank Oct 21 2007, 07:31 PM

Firstly I'd suggest that you look at your functions as graphs. Get yourself a graph package that you can enter functions into.

I will try to describe, (but it really doesn't work for me)

F(x) = x^n, n=2,3, will both look like the letter U, with x^3 having a steeper curve. x^1/2 will look like half of x^2 laying on it's side (this is actually a reflection already, of x^2, in the line y=1x.)

F(x)=|x| will look like a V. The line will be straight all the way into x=0, then it will turn sharply at 90 degrees.

F(x)=[x] is (1/x). Difficult to describe (there is a picture on this page http://www.mathsrevision.net/alevel/pages.php?page=13 )

You also need to know what transformations are. There is a brillant video for this here :
Although it deals with mobius transformations, the movemenets at the start (vertical-horizontal translations, reflections, dialations) are the ones you need (although the inversion you aren't asked to deal with).

How long do you have for the project?

/T

#### Posted by: Resurrection Oct 21 2007, 09:25 PM

I agree with Tank that some sort of graph package that would let you see the functions visually would be very helpful. By the way, is [x] really a notation for 1/x? I've never seen that terminology before. I've seen other uses for the [] operator, but these would be for techniques beyond a precalculus class. FretDancer, what's your understanding of what [x] means?

A few other points that may be of use. Note that C is a constant value.

1/ F(x + C) gives a horizontal translation of F(x) by an amount C
2/ F(x) + C gives a vertical translation of F(x) by an amount C
3/ F(-x) gives a version of F(x) reflected about the Y axis
4/ -F(x) gives a version of F(x) reflected about the X axis
5/ Even functions have F(x) = F(-x) (symmetry about the Y axis) and odd functions have F(x) = -F(x) (anti-symmetry about the Y axis)
6/ F(x/C) gives a horizontal stretch of F(x) by a factor of C
7/ C * F(x) gives a vertical stretch of F(x) by a factor of C

Try a few of these transformations on the functions you've been told to use and see the effects. Combining transformations should hopefully be obvious.

Did this help?

#### Posted by: FretDancer69 Oct 22 2007, 03:45 AM

thanks for the help and the links guys. Ill check them out

I think [x] means Step Function...

#### Posted by: Resurrection Oct 22 2007, 05:36 AM

QUOTE (FretDancer69 @ Oct 22 2007, 03:45 AM)
thanks for the help and the links guys. Ill check them out

I think [x] means Step Function...

Sounds like [x] is being used to denote the "floor" or "entier" function. If this is the case, then [x] is the biggest integer that is less than or equal to x. I'm more used to seeing it written with the top of the bracket missing, so |_ x _| is about as close as I can get with standard keyboard characters

You might want to double-check that this is the correct interpretation however!