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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.

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Presentation Transcript
warm up
Warm-Up
  • Grab a white board with a partner and the ½ yellow sheet. Have fun with the white board
continuity

Continuity

Section 1.4

3 types of discontinuities: jump, point, infinite

slide3

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.

  • Functions can be continuous at a point, on an open interval and on a closed intervals. Watch closely!

Checkout our worksheet

open intervals and discontinuity
Open Intervals and Discontinuity

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.

discussing continuity
Discussing Continuity

Remember this must happen!

What did you find to be an effective trick to determine continuity?

semi challenge
Semi -Challenge
  • Determine the value of c such that the function is continuous on the entire real line.
slide7

Is this function continuous on its domain[-1,1] which is closed? How can we test on a closed interval?

properties of continuity
Properties of Continuity

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.

applying properties of continuity
Applying Properties of Continuity

Which, if any, are continuous functions in their domains? Why or why not?

if time permits
If Time Permits
  • Begin the IVT and EVT Exploration Exercise

(or else it’s homework but we need to watch our pacing)

homework
Homework
  • Section 1.4 #8-20 even, 29-32 all, #37-51 odd, 57-64 all, 80-85 all
  • QUIZ Friday on 1.2, 1.3
  • Expect a quick quiz over continuity and its definition and testing for it next Tuesday.