Finite Math Examples

Determine if Odd, Even, or Neither
Determine if the function is even.
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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.
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Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
Apply the product rule to .
Move .
Use the power rule to combine exponents.
Add and to get .
Raise to the power of to get .
Multiply by 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.
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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.
Tap for more steps...
Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
Apply the product rule to .
Move .
Use the power rule to combine exponents.
Add and to get .
Raise to the power of to get .
Multiply by to get .
Multiply by to get .
The function is not odd because does not product the opposite function of . In other words, .
is not odd
is not odd
Since and , the function is not even and not odd.
The function is neither even nor odd
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