Upload
herbert-lynch
View
214
Download
2
Embed Size (px)
Citation preview
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.
Click icon to add picture
•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.