# Precalculus Examples

Determine if Odd, Even, or Neither
Determine if the function is even.
To check if a function is even, substitute in for and see if the resulting function is the same as the original. In other words, .
Simplify each term.
Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
The function is not even because the resulting function (after substituting in ) is not the same as the original.
is not even
is not even
Determine if the function is odd.
To check if the function is odd, substitute in for and check if the resulting function is the opposite of original function. In other words, determine if .
Simplify each term.
Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
The function is odd because is the opposite of . In other words, .
The function is odd
The function is odd
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