Question

Can someone explain to me the difference between an even and odd function?

Answer 1

Even functions follow this rule: f(-x) = f(x).

Odd functions follow this rule: f(-x) = -f(x).

Some functions are neither even nor odd, but if they are, they would follow one of the above rules.

Answer 2

and also, even function: ex) x^2, x^4, x^6 etc. (the exponents are even)
odd function: ex) x^3, x^5 etc. ( the exponents are odd)

Answer 3

Just to add to the above... if you look at the graph of a function, an even function is always symmetric about the y-axis (think about the graph of x^2). And an odd function is always unchanged by a 180 rotation about the origin (think about the graph of x^3).

Answer 4

Even functions always look exactly the same if you flip them across the y-axis.

Odd functions always look exactly the same if you rotate them 180 degrees around the origin.

Answer 5

Even functions follow this rule: f(-x) = f(x).

Odd functions follow this rule: f(-x) = -f(x).

Some functions are neither even nor odd, but if they are, they would follow one of the above rules.