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Warm-Up

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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Warm-Up

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  1. Warm-Up • Grab a white board with a partner and the ½ yellow sheet. Have fun with the white board

  2. Continuity Section 1.4 3 types of discontinuities: jump, point, infinite

  3. 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

  4. 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.

  5. Discussing Continuity Remember this must happen! What did you find to be an effective trick to determine continuity?

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

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

  8. 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.

  9. Applying Properties of Continuity Which, if any, are continuous functions in their domains? Why or why not?

  10. If Time Permits • Begin the IVT and EVT Exploration Exercise (or else it’s homework but we need to watch our pacing)

  11. 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.

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