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Homework Help: Simple f(x) equation

  1. Feb 27, 2007 #1
    1. The problem statement, all variables and given/known data
    Given f(x) = x^2. Graph f(2x)


    2. Relevant equations

    I just need to draw the graph

    3. The attempt at a solution

    What I tried was putting the x value in the equation which would give me the y value by means of the x^2 part, and the x value would double to give me my new point. This wasn't what the answer key had. Any tips?
     
  2. jcsd
  3. Feb 27, 2007 #2
    When you are asked to find f(2x), you need to substitute 2x as a whole for the original x. Will the value of f(x) really double?
     
  4. Feb 27, 2007 #3
    it becomes f(2x) = (2x)^2
     
  5. Feb 27, 2007 #4

    HallsofIvy

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    Science Advisor

    There are two ways to do this. The simplest is to do what theperthvan (and, indirectly, Tedjn) suggests: replace x by 2x. What is (2x)2?

    The other is to argue that any change before the "main" function, x2, is applied is a change in x and so changes the graph only horizontally. The value x= 1, after multiplying by 2, becomes the same as x= 2. But 1 is only 1/2 as far from the origin as 2: the whole graph of y= x2 is "squeezed" by 1/2 horizontally but not changed vertically.
     
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