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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:


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]


Can someone please explain me, or help me, PLEASE...sad.gif sad.gif
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 )

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?

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

I think [x] means Step Function... unsure.gif
QUOTE (FretDancer69 @ Oct 22 2007, 03:45 AM) <{POST_SNAPBACK}>
thanks for the help and the links guys. Ill check them out

I think [x] means Step Function... unsure.gif

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 wacko.gif

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