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Example Question #11 : Functions And Graphs
This function is:
Possible Answers:
symmetric about the origin
not symmetric
symmetric about the y-axis
symmetric about the x-axis
Correct answer:
symmetric about the y-axis
Explanation:
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.
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