![]() ![]() We see that the graph of f ( x ) f ( x ) has a hole at a. Our first function of interest is shown in Figure 2.32. We then create a list of conditions that prevent such failures. Continuity at a Pointīefore we look at a formal definition of what it means for a function to be continuous at a point, let’s consider various functions that fail to meet our intuitive notion of what it means to be continuous at a point. Intuitively, a function is continuous at a particular point if there is no break in its graph at that point. We begin our investigation of continuity by exploring what it means for a function to have continuity at a point. They are continuous on these intervals and are said to have a discontinuity at a point where a break occurs. Other functions have points at which a break in the graph occurs, but satisfy this property over intervals contained in their domains. ![]() Many functions have the property that their graphs can be traced with a pencil without lifting the pencil from the page.
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