Precalculus 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.
Find .
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Find by substituting for all occurrence of in .
Simplify each term.
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Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
A function is even if .
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Check if .
Since , the function is even.
The function is even
The function is even
Since the function is not odd, it is not symmetric about the origin.
No origin symmetry
Since the function is even, it is symmetric about the y-axis.
Y-axis symmetry
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