Chap2_Sec5

# Chap2_Sec5 - CONTINUITY Example 2(2.5 Where are each of the...

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Where are each of the following functions discontinuous? a. b. c. Why? CONTINUITY Example 2 (2.5) 2 2 ( ) 2 x x f x x - - = - 2 1 0 ( ) 1 0 if x f x x if x = = 2 2 2 ( ) 2 1 2 x x if x f x x if x - - = - =

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The figure shows the graphs of the functions in Example 2. s In each case, the graph can’t be drawn without lifting the pen from the paper—because a hole or break or jump occurs in the graph. CONTINUITY
The kind of discontinuity illustrated in parts (a) and (c) is called removable. s We could remove the discontinuity by redefining f at just the single number 2. s The function is continuous. CONTINUITY ( ) 1 g x x = +

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The discontinuity in part (b) is called an infinite discontinuity. CONTINUITY
The discontinuities in part (d) are called jump discontinuities. s The function ‘jumps’ from one value to another. CONTINUITY

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is continuous on the interval [-1, 1]. 2
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Chap2_Sec5 - CONTINUITY Example 2(2.5 Where are each of the...

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