Continuity & Discontinuity Notes

With your partner, click through the

notes and copy the visuals/

concepts using the double

entry journal format. Try to

fill in the blanks and

make conclusions based on the visuals and

questions. We will be

reviewing these together

as well, BUT TRY your best

to make conclusions.

These graphs are continuous. •What makes these graphs continuous visually?

Click icon to add picture

For continuous graphs:•All function values __________.•All limit values ____________.•The function values for every x _________ the limit values for every x.

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•What makes these graphs discontinuous visually?

These graphs are discontinuous:

•Types: point, infinite, non-existence in an interval, and jump discontinuity

Try to match up the type of discontinuity with the graph:

•A function value(s) ________ ______ ___________.

For a function/graph to be discontinuous, one of the following must apply:

•A limit value(s) ________ ______ ___________.

•A function value does not ___________ the limit value at a specific x-value.

What value would make this graph continuous where x is 0? How is this related to the limit value as x approaches 0? Therefore, when you are trying to determine what value would make a graph/equation continuous, what value are you actually looking for?

Using the same logic, what value would make this graph continuous where x=2?

2

1032

x

xxy

Go back through if necessary. And be ready to ask questions!

At this point, you should understand

the difference between

continuity and dis-

continuity. Also, you

should understand how limits are related

to continuity.