Continuity Discussion

This discussion helps build understanding of what it means for a function to be (dis)continuous at a point, as described in “Continuity at a Point” and “Types of Discontinuities” in section 2.4 of our textbook.

Please post at least one response to at least one of the following by class time on Thursday, September 17.

Part 1

Here is a sketch of the graph of a hypothetical function. Where is this function discontinuous? What requirement(s) for continuity are missing at each discontinuity? What kind of discontinuity is each? Give one or two examples of places where this function is continuous. (Interpret each tick mark on the x axis as corresponding to 1 unit if it helps you identify points on the graph.)

Part 2

Consider the function

Is this function continuous or discontinuous at x = 0?

How about x = 1?

Give some examples of x values where this function is continuous, and show why it is continuous at those values.