[crazymoose]

I'm doing calculus and unfortunately I'm stuck trying to do it before I do my grade 12 math, which means they assume I know stuff that I don't. I need a bit of help with translations and transformations.

I know:
y = f(x) is the unchanged function.
y = f(x - a) is y = f(x) moved a units right
y = f(x) + a is y = f(x) moved a units up
y = -f(x) is y = f(x) reflected along the x axis
y = f(-x) is y = f(x) reflected along the y axis
x = f(y) is y = f(x) reflected along the line y = x

And then you can combine all those and what not. Good fun.

What I need to know:
How does y = af(x)) relate to y = f(x)?
How does y = f(ax) relate to y = f(x)?

Also, what is the proper name? I don't want like 'this noms the graph and makes it littler'. I need technical terms. Like y = f(x) + a is "a vertical translation of a units upward along the y axis"

[SccHarpGirl]

Realize I'm a day late and a dollar short here, but here goes

Let's use y = square root (x) for an example function, because it's easy to work with

1. Try graphing y=2*sqrt(x) and y = (1/2)(sqrt(x)) and see what you get. Compare to y=sqrt(x). You should see 3 curvefs of differing height. They are stretched or compressed vertically by a factor of a. So I'd call this a vertical stretching or compression, because you are stretching or squeezing the function in the y direction.

Here I think it's easier to see if we use y=x^2 as our example function

2. Graph y=(2x^2) and y=(1/2*x)^2. Compare to the original function. What you should see is a parabola that has been stretched or squeeze horizontally - they are differing widths, differing by a factor of a. So I'd call this a horizontal stretching or compression transformation.

Hope that helps! You're brave to do calc without precalc - but I did the same, and came out OK So if you ever need any help, don't hesitate to ask