Question

wht maks a function odd or even

Answer 1

well there is a test.... and functions fall into 3 categories

even functions are when you substitute x = -x and you get the original function

f(-x) = f(x) e.g. f(x) = x^2 is even.... since f(-x) = (-x)^2 = x^2

odd functions occur when

f(-x) = -f(x) as an example f(x) = x^3 f(-x) = (-x)^3 = -x^3 its the negative version of the original function.

and the biggest group are neither odd nor even.

when x = -x is substituted you don't get the original function or the negative version of it..

e.g. f(x) = x^3 + x^2 f(-x) = (-x)^3 + (-x)^2 = -x^3 + x^2

which is different to both the original and the negative of the original.

hope it helps

Answer 2

geometrically
odd functions are functions that are symmetrical about the origin
even functions are functions that are symmetrical about the y-axis
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algebraically
f(-x)=f(x) <=> f is even
f(-x)=-f(x) <=> f is odd
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example of functions that are symmetric about the origin are:




example of functions that are symmetric about the y-axis are:






how about even symmetric relations.
example:


Pretending I draw perfect! :p