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Transformation of a graph

  1. Oct 21, 2006 #1
    [​IMG]

    For this graph, I'm not sure exactly how the equation y = (x³+1)² is transformed to get the graph (x³/8 + 1)². I said that it was just horizontally stretched by a factor of 8 but there has been a change in its intercepts. Also, not all the x-coordinates are changed by a factor of 8. Can anyone help clarify this for me? Thanks in advance
     
  2. jcsd
  3. Oct 21, 2006 #2

    0rthodontist

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    Compare [tex](x^3 + 1)^2[/tex]
    to [tex](\frac{x^3}{8} + 1)^2[/tex]
    The latter equals
    [tex]((\frac{x}{2})^3 + 1)^2[/tex]
    Now let's say that I plug in a value x1 to f(x) for some function f, and get a value y1 back. Now what number x2 should I plug into the function g(x) = f(x/2) to get the same value y1? This is asking, what should x2 be if you have f(x1) = f(x2 / 2)? Do you see how to apply this to your problem?
     
  4. Oct 21, 2006 #3
    Oh .. so it isn't horizontally stretched by a factor of 8 but rather a factor of 2? It seems to work out that way:

    f(x) - (1,4), (-1,0) ...
    g(x) - (2,4), (-2,0) ...

    Hmm... can someone explain why is it so? At a first glance, one would assume that the 1/8 would affect the original graph rather than 1/2
     
  5. Oct 21, 2006 #4

    0rthodontist

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    :grumpy: :grumpy:
     
  6. Oct 22, 2006 #5

    HallsofIvy

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    As was just pointed out to you, g(x) = f(x/2). x itself is not divided by
    8. That should be all the expanation you need.
     
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