What does it mean when a question says if an equation is odd, even, or neither

Even functions are functions that can map onto themselves by a reflection across the y axis

an example is f (x) = x²

odd functions are functions that are reflected across the origin (means one side is flipped across y axis not both sides)

an example is f (x) = x³

to test if it is odd or even or neither, do this test

if it is even, you can replace x with - x and get the same equation

basically if f (x) is an even function then f (x) = f (-x)

exampe

f (x) = x²

f (-x) = (-x) ²

f (-x) = x²

same thing, this is even

for an odd one, when you replace x with - x, f (x) turns to - f (x)

basically f (-x) = - f (x)

f (x) = x³

f (-x) = (-x) ³

f (-x) = - x³

neither is if it is neither of those like this one

f (x) = x²-2x

if we replace x with - x we get f (-x) = x²+2x and that is not the same function nor is it the negative of the original function

see below

It means that the equations answers are

odd (numbers 1,3,5,7,9)

even numbers (2,4,6,8,10)

or neither (0 or infinity)