In each of the following, give an example of a function f(x) with the given characteristics. You must write equations for your functions. There are many possible answers. (a) A function that is continuous at x = S and differentiable at x = 5. This answer has not been graded yet. A function that is continuous at x = 5 but not differentiable at x = 5. This answer has not been graded yet. (c) A function that is not continuous at x = 5 and not differentiable at x = 5. This answer has not been graded yet. (d) Explain why you could not be asked to find a function that is differentiable at x = 5 but is not continuous at x = 5.