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Given the functions below, compute the following values 

  1. Calculate , , and .

    can be called, informally, the Boundary Point of the piecewise function . This is because is the location where the left and the right pieces switch.

    and are on the left side of the Boundary Point, is on the right side of the Boundary Point.


  2. Calculate , , and .

    The Boundary Point is . So lies on the left side of the piecewise function while and lie on the right.

  3. Calculate , , , and .

    This function has two boundary points and three pieces: a left piece, a middle piece and a right piece.

  4. Sketch a graph of .

    Linear Piecewise, left piece, ray starting at the closed point (0, comma 0), passing though the point (negative 2 comma 2), continuing left & up, center piece, decreasing curve, opening up, coming from infinity, just right of y axis, stopping at the closed point (1, comma 5), right piece, ray starting at the open point (1, comma 4), passing through (3, comma 0), continuing right & down.