A bit of confusion I am having with compression and expansion.

1.
Original was a -5.
Compress horizontally by a factor of 1/5. New equation: y=f(5x)

2.
Expand horizontally by a factor of 3. New equation: y=f(1/3x)

3.
Compress horizontally by a factor of 1/4. New equation: y=(4x)

4.
Compress horizontally by a factor of 2/9. New equation: y=(-9/2x)

Basically what I am asking is shouldn't number 3 be EXPAND because it is a positive? It might be an error on my sheet but it is printed from my teacher, so I am right now.

Oh and shouldn't number 1's new equation be: y=f(-5x)?
It would make sense if expand for positive and compress for negative.. unless this idea is wrong..

No: compression and expansion are indeed inverse operations, but you do invert an expansion into a contraction by changing the sign, you do so by using the multiplication inverse; basically, whenever you contract by a factor n, you also expand by 1/n not -n, and when you expand by k, you also contract by 1/k not -k.

Changing the sign has nothing do with expansions or compressions; in fact, if you touch the sign, you are doing, besides stretching, another transformation: reflection.