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Difference between graphs of -f(x) and f(-x)

  1. Feb 13, 2014 #1
    It often seems as though it's backwards from what it should be, I had understood -f(x) meant to flip x and y, from positive to negative, or vice versa, and f(-x) to mean you just make x negative. If you had the points (2,2) you'd make them (-2,-2) for -f(x) and (-2,2) for f(-x) Is my understanding wrong?
  2. jcsd
  3. Feb 13, 2014 #2
    The rest of the title should be graphing.
  4. Feb 13, 2014 #3

    Stephen Tashi

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    Science Advisor

    If the point (2,2) is (x,f(x)) then (x, -f(x)) is the point (2,-2) and (x,f(-x)) can't be determined unless you know what f(-2) is. For example if f(x) = 2x -2, f(2) = 2 and f(-2) = -6. So (x,f(-x)) is (2,-6).
  5. Feb 13, 2014 #4
    Ok, that makes more sense.
  6. Feb 13, 2014 #5


    Staff: Mentor

    Assuming that you have the graph of y = f(x),
    1. The graph of y = -f(x) is the reflection across the x-axis of the graph of y = f(x).
    2. The graph of y = f(-x) is the reflection across the y-axis of the graph of y = f(x).
    3. The graph of y = -f(-x) is the reflection across the origin (that is, across both axes) of the graph of y = f(x).
    If you had the point (2, 2) on the graph of f, the point (-2, -2) would be on the graph of y = -f(-x). Note the two minus signs.
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