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How to Find the Axis of Symmetry for a Piecewise Function

Piecewise functions differ from standard functions. Standard functions are defined by one equation. Piecewise functions, however, are defined by multiple equations that are true at different areas of the function's domain. Asymmetry may be seen between two separate portions of a piecewise function, depending on its definitions. Determining the axis of symmetry for a piecewise function requires an evaluation of the function values returned from varying inputs.

Instructions

- 1
  Replace all "y" values in the piecewise function with "-y." If the value returned is the same in both cases, after the function is simplified, the axis of symmetry is the x - axis.
- 2
  Replace all "x" values in the function with "-x." Simplify the function. If the function is the same after simplification, there exists symmetry about the y - axis.
- 3
  Replace all "x" and "y" values with "-x" and "-y." If the piecewise function simplifies to a form identical to the starting function, it is symmetrical about the origin.

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