Determine algebraically whether the functions are odd, even, or neither

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01-01-2018
Mathematics

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Determine algebraically whether the functions are odd, even, or neither

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AriZenZen AriZenZen · Answer 1 · 2018-01-01T10:06:39+01:00

Switch all x variables to -x.

If the new equation is the same as before (y = x^2 + |x|) then the equation is even.

If the new equation is the exact opposite (y = x^3 --> y = -x^3) then the equation is odd.

If the equation turns out to be neither (y = x+1) then the answer is neither.

It can never be both.

Try graphing it out too! Even ones are symmetrical across the y axis. Odd ones can be rotated 180 degrees and still create the same line.