Step or Staircase Functions (Type of Piecewise Function) A piecewise function is defined by different equations on different parts of its domain. A step function is discontinuous (you need to lift your pencil off the page to graph different intervals of it) and features horizontal “pieces.” Piecewise Function Step (Staircase Function) Write a piecewise function equation from the given graph for given intervals. Writing Inequalities Write a piecewise function equation from the given graph for given intervals. Write a piecewise function equation from the given graph for given intervals. Write a piecewise function equation from the given graph for given intervals.