what is the requirement for a function to be neither odd or even?

[true dagger]

Hi! I know this might be a simple question, but i really dont understand what makes a function to be neither both someone tries to explains to me once but since im dumb i cant get it at all

If odd that means f(-x) = -x
If even that means f(-x) = x

Now, how can a function be neither? Seems paradoxical to me

[nova galleon]

And odd function : f(-x) = -f(x)
for all x real
An even function : f(-x) = f(x)
for all x real

"for all x" is very important

The first function is even. Graphicly, the curve is symmetric along the y-axis
We have
f(1) = 1
and f(-1) = 1

f(2) = 4
and f(-2) = 4

f(3) = 9
f(-3) = 9

...
Each couple of opposed numbers that we send to f is transformed by f into the sale number

the second is odd.
graphicly the curve us symetric at the origin.
f(1) = 1
f(-1) = -1

f(2) = 8
f(-2) = -8

...
Two opposed still being two opposed by applying f

and the last function
is neither odd nor even
f(2) = 0
but f(-2) = -4

[true dagger]

So its neither if the graph is not symmetrical to neither x or 0 or not symmetrical at all?

Sorry if my english is bad

Ahh i think i started to get it now

[nova galleon]

what is your native language

[true dagger]

Indonesian

[nova galleon]

ah ok, french for me

and yes the function isn't symmetric along the y-axis (axial symmetry) even function

and isn't symmetric with (0,0) (central symmetry) odd function

the function is neither odd nor even

[true dagger]

Got it! Thanks! Much appreciated 🙏

[nova galleon]

!done

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[true dagger]

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