It makes sense that the graph's behavior would change when transitioning from positive to negative, as well as the other special threshold in this case which is the number 1 (since we are multiplying). Take a number X, where (inf. > abs(x) > 1), here it means that it is raised to a positive power, and (1 > abs(x) > 0) means a negative power.
Scaling (stretching) depends on the absolute value of the scaling factor, and how it relates to the number one. Flipping depends on whether the factor is positive, or negative. Apply at the same time and you get all those changing intervals, notice the change at each threshold.
(1 - inf.) = compressed, non-flipped.
[1] = equal, non-flipped.
(0 - 1) = stretched , non-flipped.
[0] = no graph i.e. a single point.
(-1 - 0) = stretched , flipped.
[-1] = equal, flipped.
(-inf. - -1) = compressed, flipped.
Also, the same does happen with vertical stretching. However, in the case of shifting, we are not multiplying, so the number 1 is no longer a critical point of concern, only the sign of the factor.
