no, i used f(1) as an example. it was just an illustration, nothing more. i just wanted to show you why we have to choose larger values of x (hence stretch) or choose smaller values of x (hence shrink)

that discussion works for vertical stretches or shrinkings.*sigh* my professor didn't explain it the way you are in the least bit. He just told us one gets closer to the x-axis and the other gets further away.

Can you by any chance you can just tell me how to do horizontal stretching and shrinking in a really easily understandable way?Vertical Stretching:

Given a function f(x), we obtain cf(x), where c is a constant, by stretching the graph vertically by a factor of c. that is, we leave the x-values the same, and multiply all y-values by c.

Vertical Shrinking:

Given a function f(x), we obtain (1/c)f(x), where c is a constant, by shrinking the graph vertically by a factor of c. that is, we leave the x-values the same, and multiply all y-values by (1/c).

Horizontal Shrinking:

Given a function f(x), we obtain f(cx), where c is a constant, by shrinking the graph horizontally by a factor of c. that is, we leave the y-values the same, and multiply all x-values by (1/c).

Horizontal Stretching:

Given a function f(x), we obtain f((1/c)x), where c is a constant, by stretching the graph horizontally by a factor of c. that is, we leave the y-values the same, and multiply all x-values by c.

so you see, it's like we want to get back to f(x) if a constant interferes. since y = f(x), if we get f(cx), we multiply x by (1/c) to get f(c(1/c)x) = f(x). so it shrinks, since we assume c >= 1, so we are in effect multiplying by something less than 1

calm down. everything will be fineI feel like i'm getting more and more confused and I have my first major test on this stuff tomorrow.