How do different transformations affect g(x)?

[flyingpig]

Homework Statement

Back in pre-calc, I learned that f(x) can be transformed in the ways of

y = af(bx +c) + d

But very often I come across nastier functions that aren't transformed by scalars, but instead let's say

y = g(x)

what does the transformation do to g(x)?

1. g(x) + x

2. xg(x)

3. $$\sqrt{g(x)}$$

4. sin(x)g(x) (in the case of g(x) being any elementary trig function)

The Attempt at a Solution

not a clue

 

[rock.freak667]

I don't think that there are transformations for those functions. g(x) would be an entirely different function.