Algebra Examples

Determine if the function is odd, even, or neither in order to find the symmetry.
1. If odd, the function is symmetric about the origin.
2. If even, the function is symmetric about the y-axis.
Check if the function is odd. In other words, .
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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.
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Apply the product rule to .
Raise to the power of 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 the function is not odd, it is not symmetric about the origin.
No origin symmetry
Check if the function is even. In other words, .
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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 .
The function is even because the resulting function (after substituting in ) is equivalent to the original.
The function is even
The function is even
Since the function is even, it is symmetric about the y-axis.
Y-axis symmetry
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