Piecewise functions

• How Do You Graph a Sine Function Increased on One Side?
  There is no unique graph until “increased” is defined. Compare one-sided amplitude changes, vertical shifts, and smooth added terms.
• How to Differentiate a Piecewise Function
  Differentiate each formula on its interval, then test every breakpoint with continuity and matching one-sided derivatives to determine whether the derivative exists.
• How Do You Differentiate a Triangle Wave?
  Differentiate a triangle wave by finding the slope of each linear segment; learn why its derivative is a square wave and is undefined at corners.