Precalculus Help, PLEASE HELP ME!!! 
Precalculus Help, PLEASE HELP ME!!! 
Oct 21 2007, 06:13 AM
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#1


GMC:er Group: Passive Posts: 2.442 Joined: 11June 07 From: Honduras Member No.: 2.062 
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:
F(x) = x^n, n=2,3,1/2 F(x) = x F(x) = [x] _______________________ Can someone please explain me, or help me, PLEASE... This post has been edited by FretDancer69: Oct 21 2007, 06:21 AM  Playing Guitar Since: December 2006 


Oct 21 2007, 07:31 PM
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#2


GMC Veteran Group: GMC Senior Posts: 666 Joined: 20August 05 From: Shropshire UK Member No.: 5 
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 : https://www.youtube.com/watch?v=JX3VmDgiFnY Although it deals with mobius transformations, the movemenets at the start (verticalhorizontal 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 


Oct 21 2007, 09:25 PM
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#3


GMC:er Group: Members Posts: 202 Joined: 22May 07 Member No.: 1.906 
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) (antisymmetry 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? This post has been edited by Resurrection: Oct 21 2007, 09:27 PM  QUOTE If you think you can, you can. And if you think you can't, you're right. 


Oct 22 2007, 03:45 AM
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#4


GMC:er Group: Passive Posts: 2.442 Joined: 11June 07 From: Honduras Member No.: 2.062 
thanks for the help and the links guys. Ill check them out
I think [x] means Step Function...  Playing Guitar Since: December 2006 


Oct 22 2007, 05:36 AM
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#5


GMC:er Group: Members Posts: 202 Joined: 22May 07 Member No.: 1.906 
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 doublecheck that this is the correct interpretation however!  QUOTE If you think you can, you can. And if you think you can't, you're right. 


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