Finding Symmetries - High School Math
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Question
This function is:
This function is:
Answer
A function's symmetry is related to its classification as even, odd, or neither.
Even functions obey the following rule:
Because of this, even functions are symmetric about the y-axis.
Odd functions obey the following rule:
Because of this, odd functions are symmetric about the origin.
If a function does not obey either rule, it is neither odd nor even. (A graph that is symmetric about the x-axis is not a function, because it does not pass the vertical line test.)
To test for symmetry, simply substitute 
into the original equation.
Thus, this equation is even and therefore symmetric about the y-axis.
A function's symmetry is related to its classification as even, odd, or neither.
Even functions obey the following rule:
Because of this, even functions are symmetric about the y-axis.
Odd functions obey the following rule:
Because of this, odd functions are symmetric about the origin.
If a function does not obey either rule, it is neither odd nor even. (A graph that is symmetric about the x-axis is not a function, because it does not pass the vertical line test.)
To test for symmetry, simply substitute
Thus, this equation is even and therefore symmetric about the y-axis.
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