Precalc0105to0107-page4

Precalc0105to0107-page4 - 1, 2 ± ² ³ ´ . • We obtain...

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(Section 1.5: Piecewise-Defined Functions; Limits and Continuity in Calculus) 1.5.4 ± 2 is included in the subdomain ± 2, 1 ² ³ ) . Therefore, the endpoint ± 2, 4 () is included in this piece, and we plot it as a filled-in circle. 1 () 2 = 1 , so the right endpoint of this piece is at 1, 1 () . •• Why do we use the top rule, instead of the bottom rule? See Part F. • 1 is excluded from the subdomain ± 2, 1 ² ³ ) . Therefore, the endpoint 1, 1 () is excluded from the piece, and we plot it as a hollow circle. Bottom rule: We will graph y = x + 1 on the subdomain
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Unformatted text preview: 1, 2 ± ² ³ ´ . • We obtain a line segment . • 1 ( ) + 1 = 2 , so the left endpoint of this piece is at 1, 2 ( ) . • 2 ( ) + 1 = 3 , so the right endpoint of this piece is at 2, 3 ( ) . • Both 1 and 2 are included in the subdomain 1, 2 ± ² ³ ´ . Therefore, the endpoints 1, 2 ( ) and 2, 3 ( ) are included in this piece, and we plot them as filled-in circles. The graph of f is below. In calculus , we say that f has a jump discontinuity at 1 x = 1 ( ) . (See Part G.) §...
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This document was uploaded on 12/29/2011.

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