Results 1 to 2 of 2
Like Tree1Thanks
  • 1 Post By MacstersUndead

Thread: Making sense of horizontal and vertical scaling and shifting

  1. #1
    Newbie
    Joined
    Apr 2019
    From
    ????
    Posts
    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.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Jan 2009
    Posts
    417
    Thanks
    79

    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)
    Last edited by MacstersUndead; Apr 15th 2019 at 06:51 PM.
    Thanks from topsquark
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: Mar 21st 2014, 06:00 PM
  2. Making sense of it all
    Posted in the Algebra Forum
    Replies: 3
    Last Post: Aug 18th 2013, 11:16 PM
  3. horizontal or vertical?
    Posted in the Geometry Forum
    Replies: 5
    Last Post: Sep 7th 2009, 09:18 AM
  4. Geo HW not AT ALL making sense
    Posted in the Geometry Forum
    Replies: 7
    Last Post: Dec 7th 2008, 07:18 PM
  5. Not making sense...probability
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: Oct 13th 2008, 04:54 PM

/mathhelpforum @mathhelpforum