What are the defintions for vertical/horizontal compressions and vertical/horizontal expansions?

If you are referring to compressions and expansions on a graph (transformations), then compressions occur when the graph is shrunken or scaled down. This is usually done with a number (for example a number less than 1 and greater than 0). By applying this to the x or y component you will get a vertical or horizontal compression. In contrast, an expansion (vertically or horizontally) is when a graph is stretched (either by its y or x value). This is done when either the y or x component is multiplied by a number greater than 1 (positive number).

To be more specific:

Vertical compressions and expansions are

along the y-axis and involve the y component.

Horizontal compressions and expansions are

along the x-axis and involve the x component.

Hope this helps and good luck with your homework!