The condition of continuity-that the function

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Make the given changes in the indicated examples of this section. Then solve the resulting problems.

In Example 2, change the denominator to x + 2 and then determine the continuity.

EXAMPLE 2 Function discontinuous at x = 2

The function is not continuous at x = 2 When we substitute 2 for x , we have division by zero. This means the function is not defined for the value x = 2 The condition of continuity-that the function must exist-is not satisfied. The graph of the function is shown in Fig. 23.2. From a graphical point of view, a function that is continuous over an interval has no "breaks" in its graph over that interval. This means that the function is continuous over the interval if we can draw its graph without lifting the marker from the paper. If the function is discontinuous for some value or values over an interval, a break occurs in the graph because the function is not defined or the definition of the function leads to an instantaneous "jump" in its values.

Reference no: EM131100240

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