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Concept

Odd Function

An odd function is a function for which the value of is equal to the value of for all the values in its domain. It is like if the function allows moving the negative sign from the input to the output.

The graph of an odd function is symmetric about the origin, meaning that the graph looks the same after a rotation about the origin. The functions  and are two examples of odd functions.
Graphs of f(x)=x and graph of g(x)=x^3
Notice that if a function is odd and the point is on the graph, then the point is also on the graph. A function can be odd, even, or neither.

Extra

Determining If a Function is Odd
To determine algebraically whether a function is odd, substitute into the function rule and simplify. If the resulting expression is equal to then the function is odd; otherwise, it is not. For example, consider the following function.
Substitute for and simplify.
Since the given function is odd.
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