Determining if a function is even or odd can be done quickly with these simple steps:
- Substitute -x: Replace x in the function with -x. If the resulting function is identical to the original, it’s even. Example: f(x) = x². Substitute -x: f(-x) = (-x)² = x².
- Check Symmetry: Graphically, even functions are symmetric about the y-axis. Odd functions have rotational symmetry around the origin. Wolfram Alpha helps visualize this.
- Verify -f(x): For an odd function, substituting -x should yield -f(x). Example: f(x) = x³ -> f(-x) = -x³ = -f(x).
Using these steps will help you determine the nature of a function quickly.