Determine whether each function is even, odd, or neither. See Example 5. ƒ(x)=x^3-x+9

Key Concepts

Even Functions

A function is classified as even if it satisfies the condition f(-x) = f(x) for all x in its domain. This means that the graph of the function is symmetric with respect to the y-axis. A common example of an even function is f(x) = x^2, where substituting -x yields the same output as substituting x.

Odd Functions

A function is considered odd if it meets the condition f(-x) = -f(x) for all x in its domain. This indicates that the graph of the function is symmetric with respect to the origin. An example of an odd function is f(x) = x^3, where substituting -x results in the negative of the output for x.

Neither Even Nor Odd Functions

A function is classified as neither even nor odd if it does not satisfy the conditions for either classification. This means that f(-x) does not equal f(x) and also does not equal -f(x). An example would be f(x) = x^3 - x + 9, as it does not exhibit symmetry about the y-axis or the origin.