Practice Symmetric Functions in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A symmetric function is one that remains unchanged (or changes in a predictable way) under specific variable transformations. Even functions satisfy and are mirror-symmetric about the y-axis; odd functions satisfy and have 180-degree rotational symmetry about the origin.
Even functions are symmetric about the y-axis: . Odd functions have 180ยฐ rotational symmetry about the origin: .
Showing a random 20 of 50 problems.
Example 1
easyIs the product even, odd, or neither?
Example 2
mediumIf and , find .
Example 3
mediumIs a symmetric function of and ?
Example 4
mediumClassify .
Example 5
hardIf , , and , find .
Example 6
mediumClassify .
Example 7
hardDetermine whether the function is symmetric, anti-symmetric, or neither under swaps of variables.
Example 8
mediumIs even, odd, or neither (for )?
Example 9
mediumIf is even and , what is ?
Example 10
mediumThe product of an even function and an odd function is even, odd, or neither?
Example 11
hardIf is odd, prove that is even.
Example 12
easyIs even or odd?
Example 13
mediumDecompose into even and odd parts.
Example 14
easyIs even, odd, or neither?
Example 15
easyIf is even, what symmetry does its graph have about the -axis?
Example 16
easyIs the function symmetric in and ?
Example 17
challengeGiven roots of , find using Newton's identities.
Example 18
easyIs even or odd?
Example 19
easyIs even, odd, or neither?
Example 20
mediumIf is odd and continuous at , what must equal?