Tuesday, February 2, 2010

I see, and I see Math.

A not one-to-one function

Not a one-to-one function

A continuous and Differentiable function

Invertible function

An invertible function

Continous and Differentiable

Not Continuous and not Differentiable

Not continous and not differentiable

Continuous but not Differentiable

Continuous but not differentiable




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3 comments:

  1. dammitimmadFebruary 3, 2010 at 9:42 PM

    Hey Marley,
    Super creative photos (a nail clipper, I would have never thought of that, so awesome!!). And if you don't mind me saying, that looks like a very comfortable rug. I like your use of every day objects to portray the required examples. I admire that you were able to take ordinary things and look beyond their face values. I think this is all very solid except for your invertible function.
    When you invert a parabola, it is not one-to-one, thus it is not invertible. Only half of it (ie left of the x axis or right of the x axis) is invertible. You can tell this because the parabola fails the horizontal line test, which means that if it was inverted, it would fail the vertical line test. I created a graph on winplot to show you but as i just discovered, pictures cannot be uploaded to comments. If you are interested though, here is a link to an image that will show you what I'm talking about.

    http://library.thinkquest.org/2647/media/parainv.gif

    Great job,
    dammitimmad

    ReplyDelete
  2. MarleyFebruary 7, 2010 at 12:51 PM

    dammitmmad, Thank you.
    I didn't think about the horizontal and vertical line tests.
    And also, thank you for the link, it was very clear and helpful.
    I'm thinking about interchanging the picture for "continuous and differentiable" and "invertible function" since a linear function is invertible and a parabola is continuous and differentiable.

    Thank you
    Marley.

    ReplyDelete
  3. dammitimmadFebruary 7, 2010 at 8:08 PM

    Great thinking

    ReplyDelete

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