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8-10.
  1. Use the graph of g(x) at right to answer the following questions. Provide reasons for each value found. Homework Help ✎

    1. For what values of x is g(x) undefined?

    2. For what values of x is g(x) discontinuous?

    3. For what values of x is g(x) non-differentiable?

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

There are three conditions of continuity.
If any of these conditions are violated, then the function is NOT continuous at the value of x.

2. f(a) exists. This means that f(a) is finite.

y = g(x) has exactly three points in which it is discontinuous. Where are they?

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.