Horizontal Stretches/Compression (Math Question).

[miz1q2w3e]

Jay520 said:

miz1q2w3e said:

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.

Huh? The same doesn't happen with vertical stretching. The direction of the graph correlates with whether the positivity/negativity of A in Af(x).

In vertical stretching, as A decreases the graph is pulled downward. Even as A goes negative, the graph continues to go downward. The opposite is true when positive of course.

This is different from horizontal stretching. As A in f(Ax) decreases, the graph widens away from the Y-axis (assuming the graph is symetrical along the Y axis), but once it hits zero, it stops widening away from the Y-axis and begins to shrink toward the Y-axis

Another thing; yes it begins to shrink, but it is still technically stretched at the point after it hits zero but before it goes past negative 1. Whether is is expanding or shrinking at that moment depends on which way you are coming from.