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

  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. The rest of the title should be graphing.
     
  4. Stephen Tashi

    Stephen Tashi 4,398
    Science Advisor
    2014 Award

    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. Ok, that makes more sense.
     
  6. Mark44

    Staff: Mentor

    No.
    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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