Even and odd functions
Decide whether the function f is even, odd or neither even nor odd.
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An even function gives the same value for x and for −x, for example 2² = 4 and (−2)² = 4. Its graph is symmetric about the y-axis. An odd function gives the opposite value for −x: (−2)³ = −8. Its graph is symmetric about the origin.
What does this generator do?
At the easy level it shows a polynomial, for example x⁴ − 3x² or x³ + 2. At the medium level functions with absolute value and fractions are added. At the hard level you decide from a graph, or you get a formula with a restricted domain.
How to use it
1) First check the domain: it must be symmetric about zero, otherwise the function is neither even nor odd. 2) Substitute −x for x and simplify. 3) If you get the original formula, the function is even. If you get the formula with every sign flipped, it is odd. 4) For a graph, look for symmetry about the y-axis or about the point (0, 0).