# Find the Symmetry f(x)=x^5-3x 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 .
Find by substituting for all occurrence of in .
Simplify each term.
Apply the product rule to .
Raise to the power of .
Multiply by .
A function is even if .
Check if .
Since , the function is not even.
The function is not even
The function is not even
A function is odd if .
Find .
Multiply by .
Apply the distributive property.
Multiply by .
Since , the function is odd.
The function is odd
The function is odd
Since the function is odd, it is symmetric about the origin.
Origin Symmetry
Since the function is not even, it is not symmetric about the y-axis.
No y-axis symmetry
Determine the symmetry of the function.
Origin symmetry
Find the Symmetry f(x)=x^5-3x

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