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Use the graph of below to answer the following questions. Provide reasons for each value found.

  1. For what values of is undefined?

    Are there any values for which there is no existing -value?

  1. For what values of is discontinuous?

    There are three conditions of continuity.
    If any of these conditions are violated, then the function is NOT continuous at the value of .
    1.  exists. This means that  and that limit is finite.
    2. f(a) exists. This means that f(a) is finite.

    has exactly three points in which it is discontinuous. Where are they?

  2. For what values of is non-differentiable?

    A function is NOT differentiable where it is not continuous and/or where the derivative is not continuous. Examples of points of non-differentiablity include: cusps, endpoints, jumps, holes and vertical tangents.