What is the rule for dilation? Like, for translation, you add/subtract the units being translated from the x and y value. what do you do for dilation??

Putting a coefficient other than 1 in front of the x or y term (before it is raised to any power) will expand or "squash" the plotted curve in either the x or y direction.

I have never heard this referred to as 'dilation', but I assume that is what they mean here.

For a dilation, you need to multiply the x and y coordinates of each point by a scale factor. The scale factor determines how much the figure is magnified or shrunk. The rule for dilation is as follows:

1. If the scale factor is greater than 1, the figure will be enlarged. Multiply both the x and y coordinates of each point by the scale factor.

Example: Let's say you have a point (2, 3) and the scale factor is 2. Multiply both x and y coordinates by 2:
New coordinates = (2 * 2, 3 * 2) = (4, 6)

2. If the scale factor is between 0 and 1, the figure will be reduced. Multiply both the x and y coordinates of each point by the scale factor.

Example: Using the same point (2, 3) and a scale factor of 0.5:
New coordinates = (2 * 0.5, 3 * 0.5) = (1, 1.5)

3. If the scale factor is negative, the figure will be reflected across the origin. In this case, multiply both the x and y coordinates by the absolute value of the scale factor, and then change the sign of both coordinates.

Example: Consider the point (2, 3) and a scale factor of -2:
New coordinates = (-2 * |-2|, -3 * |-2|) = (-4, -6)

To summarize, for dilation:
- If the scale factor is greater than 1, multiply both coordinates by the scale factor.
- If the scale factor is between 0 and 1, multiply both coordinates by the scale factor.
- If the scale factor is negative, multiply both coordinates by the absolute value of the scale factor and change the sign of both coordinates.