Warm-Up . Grab a white board with a partner and the ½ yellow sheet. Have fun with the white board. Continuity. Section 1.4. 3 types of discontinuities: j ump, point, infinite.
3 types of discontinuities: jump, point, infinite
A function f is continuous at x = c if there is no interruption in the graph of f at csuch as a hole, jump, or gap.
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Watch out for piece-wise and rational functions. Removable Discontinuity: points because they can be refilled by simply restating a domain.Non-Removable Discontinuity: infinite, jumps because you can’t fix this domain whatsoever.
Remember this must happen!
What did you find to be an effective trick to determine continuity?
Is this function continuous on its domain[-1,1] which is closed? How can we test on a closed interval?
What this says is that if f and g are both continuous functions by themselves at c, when they do they above operations together, then the resulting new function is also continuous no matter what and you don’t need to test.
Which, if any, are continuous functions in their domains? Why or why not?
(or else it’s homework but we need to watch our pacing)