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Problem 75 Hard Difficulty

Determine whether $ f $ is even, odd, or neither. If you have a graphing calculator, use it to check your answer visually.

$ f(x) = \dfrac{x}{x + 1} $

Answer

The function is neither odd nor even.

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Video Transcript

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