Section 38: Continuity and End Behavior

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Section 3-8 Continuity and End Behavior
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Types of Graphs

• Discontinuous there is a break somewhere in the
  graph
• Continuous no break in the entire graph
• Note all polynomial functions are continuous

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Example

• f(x) x2 4 (x 2)(x-2) x-2
• x2 (x2)
• x ? -2 hole at (-2,-4)
• Discontinuous!

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Types of Discontinuity
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f(x) x if x0 x2 if xlt0

• Segmented Definition
• (piecewise function)
• Continuous

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• y x .
• x3
• Infinite discontinuity

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Continuous or Discontinuous?

• y 3x2 x 7
• f(x) 3x x
• y -1
• 3x2

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End Behavior is the behavior of f(x) as x
becomes very large.

• f(x) x3 3x2 x 3
• as x??, f(x) ??
• as x?-?, f(x) ?-?

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f(x) a0xn a1xn-1 a leading
coefficient n highest exponent
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Increasing vs. Decreasing

• Determines the intervals for which the function
  is inc./dec.
• h(x) x3 x2 x 4
• Find critical points (max./min.)
• h'(x) 3x2 2x 1 0
• (3x-1)(x1) 0
• x 1/3 x -1

-? lt x lt-1 inc. -1 lt x lt1/3 dec. 1/3 lt
x lt? inc.
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Without the graph test a point in each interval
to determine slope of tangent.
pos. inc.
neg. dec.
pos. inc.
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Homework

• P.170 171
• 14-28E, 31-32, 37, 39, 40, 42
• 35 e.c. (turn in)