# Thread: Making sense of horizontal and vertical scaling and shifting

1. ## Making sense of horizontal and vertical scaling and shifting

Simple memorization would be OK to just solve problems, but I am trying to understand the concepts. Where to begin? In this video, https://www.youtube.com/watch?v=kyq0VKPHiJQ, Patrick wants us to compare the stretching and compressing to giving the new inputs the same original values of the original inputs once all other operations are applied. This is stated at around 1:51, with y = f(2(-1)). He doesn't provide anything to relate the why of splitting the coordinates in half, and the entire aforementioned trick falls apart with the piece-wise portions of the function. It isn't compatible. Anything multiplied by 0 is 0, but it's counterintuitive to leave it like that as if the graph is tethered to it. Would it not eventually completely straighten out once shifted enough? The piece-wise line remains tethered to -1 without changing as well, which is as confusing as the 0. Also, that first piece-wise line suddenly starts with an inclusive point and remains with that inclusive point for seemingly no reason. At 4:34, he changes the function to y = f((1/2)x), and just skips to using the doubled points without giving a way to determine why it's actually double the points.

With regards to shifting, what way is there to reach the conclusion that y = (x-2)^2, for example, doesn't just mean the opposite of what is actually stated? That is, when the horizontal shift is -2, in this case, it's just 2 for no reason or because we are told the opposite is false.

When it comes to compression and stretching, the compression of y coordinates looks like stretching to me.

2. ## Re: Making sense of horizontal and vertical scaling and shifting

I couldn't write it as beautifully as this stack exchange post, so I'll use it. https://math.stackexchange.com/quest...tions-reversed
It only looks like x and y transformatins are different, but they work in the same way.

Another way to think of it is to look at x,y t-tables and check what values x are required to get original values y, though this way is very informal.
Consider
f(x) = x^2 to g(x) = (x-2)^2. For f(x) y=1 when x=1. For g(x) y=1 when x=3. x had to be 2 more for g(x) to attain the same y-value. (ie. shift 2 units to the right)

Consider
f(x) = x^2 to g(x) = ((1/2)x)^2. For f(x) y=1 when x=1. For g(x) y=1 when x=2. x had to be 2 times more for g(x) to attain the same y-value. (ie. horizontal stretch by a factor of 2)