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Use the graph of at right 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?

  2. 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 .

    2. exists. This means that is finite.

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

  3. 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-differentiability include cusps, endpoints, jumps, holes, and vertical tangents.