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So here we have function f of X, and
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we want to know if it's odd, even or
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neither. And remember that odd functions have this property
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up of the opposite of X is equal to the
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opposite of F of X. So opposite X values
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have opposite. Why values? And that means you're
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going to see origin, symmetry and for even functions
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opposite X values have the same y value, so
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that means you're going to see why. Access symmetry
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. So what we want to do for this function
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is we want to find f of the opposite of
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X and find out if it's the same as or
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the opposite of f of X or neither. So
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when we substitute the opposite of X in for X
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in both spots, we get the opposite of X
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over the opposite of X plus one. Now that's
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not the same as the original, and that's not
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the opposite of the original. It's neither, so
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we're going to determine that this one is neither on
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nor even now. We can also verify that with
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a graphing calculator, so we type the function into
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why equals and then we graph. You can see
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that this does not have y axis symmetry, and
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it does not have origin symmetry, so it's neither