# Find the Symmetry f(x)=(x^2-81)/x 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 the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
Simplify with factoring out.
Move the negative in front of the fraction.
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Rewrite as .
Factor out of .
Simplify the expression.
Rewrite as .
Multiply by .
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 .
Simplify the numerator.
Rewrite as .
Since both terms are perfect squares, factor using the difference of squares formula, where and .
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
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