Use a graph to determine whether the given function is continuous on its domain. If...

Use a graph to determine whether the given function is continuous on its domain. If it is not continuous on its domain, list the points of discontinuity. HINT [See Example 1.]

Solution

a and b. The graphs of h and k are shown in Figure 10.

Even though the graph of h is made up of two different line segments, it is continuous at every point of its domain, including x = 1 because

The domain of f consists of all real numbers except 0 and f is continuous at all such numbers. (Notice that 0 is not in the domain of f, so the question of continuity at 0 does not arise.) Thus, f is continuous on its domain.