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.
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.
Hey Marley,
ReplyDeleteSuper 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
dammitmmad, Thank you.
ReplyDeleteI 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.
Great thinking
ReplyDelete