WEBVTT
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Okay, so we have f of X equals X
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over X squared plus one. And we want to
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know if it's odd, even or neither. So
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remember that for odd functions, opposite X values give
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you opposite. Why values? And they have origin
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, symmetry and for even functions opposite X values give
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you the same. Why values? And so they
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have y axis symmetry. So let's investigate for our
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function. And let's figure out what f of the
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opposite of exes will it be the same or the
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opposite, or neither compared to the original. So
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what we need to do is substitute the opposite of
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X in for X in our function, and it
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will look like that. And then we can simplify
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. And we know that the opposite of X squared
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is just equivalent to X squared. So this looks
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like the opposite of our original function. Therefore,
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since half of the opposite of X equals the opposite
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of F of X, we have an odd function
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. So now when we look at the graph on
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the calculator, we should expect to see something that
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has origin symmetry. So we grab a calculator and
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type in the function and I'm going to try Zoom
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six for a standard negative 10 to 10 window.
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And here's how it looks. We could even change
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the window dimensions if we want. Maybe different y
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values. Let's say negative 3 to 3. Okay
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, that definitely looks like it has symmetry about the
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origin, so that confirms that it is an odd
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function.