transformations for graphs - precalculus The problem is for homework,  but I will change the problem a bit so as to try to be able to do it by myself from what someone or some people will answer here.  Ok.

Let f be a function whose domain is [0,3] and range is [-3,0]. For each function g below, describe the transformations necessary to obtain the graph of g from the graph of f :

(a) g(x) = 3f(x-4) + 3   /////
(b) g(x) = -3(f(-x) - 3)

Im not sure of a couple things,  in (b) f(-x) what does it become,  and the 3f in (a) what do I do with that multiply it by the range?

Bijan
You should brush up on the general principles, like say here: http://www.purplemath.com/modules/fcntrans.htm

In (a), multiplying $f(x-4)$ by 3 will stretch the graph vertically by a factor of 3. It's true that the endpoints of the range of $f(x-4)$ (which is not the same as the range of $f(x)$) will be multiplied by 3; and so will all the y-values of the output.

In (b), the graph of $f(-x)$ is the same as the graph of $f(x)$ having been reflected across the y-axis. If $h(x) = f(-x)$, and for example $f(2) = 0$ (so $f$ has a point at $(2,0)$), then $h(-2) = 0$ (so $h$ has a point at $(-2, 0)$), and so forth.
You should brush up on the general principles, like say here: http://www.purplemath.com/modules/fcntrans.htm

In (a), multiplying $f(x-4)$ by 3 will stretch the graph vertically by a factor of 3. It's true that the endpoints of the range of $f(x-4)$ (which is not the same as the range of $f(x)$) will be multiplied by 3; and so will all the y-values of the output.

In (b), the graph of $f(-x)$ is the same as the graph of $f(x)$ having been reflected across the y-axis. If $h(x) = f(-x)$, and for example $f(2) = 0$ (so $f$ has a point at $(2,0)$), then $h(-2) = 0$ (so $h$ has a point at $(-2, 0)$), and so forth.