Examples

Find the Symmetry
Step 1
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.
Step 2
Find .
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Step 2.1
Find by substituting for all occurrence of in .
Step 2.2
Apply the product rule to .
Step 2.3
Raise to the power of .
Step 2.4
Multiply by .
Step 3
A function is even if .
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Step 3.1
Check if .
Step 3.2
Since , the function is not even.
The function is not even
The function is not even
Step 4
A function is odd if .
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Step 4.1
Multiply by .
Step 4.2
Since , the function is odd.
The function is odd
The function is odd
Step 5
Since the function is odd, it is symmetric about the origin.
Origin Symmetry
Step 6
Since the function is not even, it is not symmetric about the y-axis.
No y-axis symmetry
Step 7
Determine the symmetry of the function.
Origin symmetry
Step 8
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