Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By SlipEternal

Thread: Transformations of f(x)

  1. #1
    Member
    Joined
    May 2010
    Posts
    100

    Transformations of f(x)

    So, I am working with my son on transformations of functions.
    He is ok with stretches and translations in the y direction but when we look at f(ax) or f(x+a) where the 'opposite' seems to happen to what he expects he gets lost! Anyone got a good way of thinking about this that can help him understand what is happening and why?
    What is the best function to pick? I realised f(x) = x^2 is confusing!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,834
    Thanks
    1087

    Re: Transformations of f(x)

    Let's compare f(ax) to f(x). Let's compare input to output:

    $\begin{matrix}x & | & f(x) & | & f(2x) \\ -- & | & ---- & | & ---- \\ -5 & | & f(-5) & | & f(-10) \\ -3 & | & f(-3) & | & f(-6) \\ -1 & | & f(-1) & | & f(-2) \\ 0 & | & f(0) & | & f(0) \\ 1 & | & f(1) & | & f(2) \\ 3 & | & f(3) & | & f(6) \\ 5 & | & f(5) & | & f(10)\end{matrix}$.

    So, when $a=2$, you get a compression of the graph by a factor of 1/2 because you only need half the value of $x$ to get the same input to the function. If you want the input to the function to be $-5$, you need to use the x-value of $-2.5$ because $-2.5\cdot 2 = -5$.

    Similarly create a chart for $f(x+a)$. Consider what happens when $a > 0$. What needs to happen to $x$ to get the same input to $f$?

    Next, consider what happens when $a<1$ for $f(ax)$ or when $a<0$ for $f(x+a)$.

    That is how it helped me to think about it.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2010
    Posts
    100

    Re: Transformations of f(x)

    I see, suppose i have y= f(x) and f(a)=k then if i consider y= f(2x) , then x would have to be 0.5a in order to get same output k, i.e. f(2(0.5a))= f(a)= k
    It's subtle because we now need to shift our thinking to ' what input gives the same output' rather ' how has the output changed?'
    Am i making a meal out of this?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    2,834
    Thanks
    1087

    Re: Transformations of f(x)

    Quote Originally Posted by rodders View Post
    I see, suppose i have y= f(x) and f(a)=k then if i consider y= f(2x) , then x would have to be 0.5a in order to get same output k, i.e. f(2(0.5a))= f(a)= k
    It's subtle because we now need to shift our thinking to ' what input gives the same output' rather ' how has the output changed?'
    Am i making a meal out of this?
    Exactly!
    Thanks from rodders
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Need Help on transformations!
    Posted in the Algebra Forum
    Replies: 1
    Last Post: Feb 3rd 2013, 04:18 PM
  2. Replies: 2
    Last Post: Oct 28th 2012, 09:16 AM
  3. Transformations
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: Jul 27th 2010, 10:39 PM
  4. transformations
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Apr 27th 2009, 10:13 PM
  5. Transformations
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: Apr 23rd 2009, 12:20 AM

/mathhelpforum @mathhelpforum