A graph often helps determine continuity of piecewise functions, but we should still examine the algebraic representation to verify graphical evidence.
{ | x^{2} | x < -1 | |
f(x) = | x | -1 x < 1 | |
-cos(x) | x 1 |
appears in the Field Guide section on piecewise functions. It is continuous at all points with the exception of x=-1, where the "pieces" do not fit smoothly together. Note that f(x) is continuous at x=1 because
lim x = | lim cos(x) | = 1 = f(1). |
x --> 1^{-} | x --> 1^{+} |
{ | e^{x} | x < 0 | |
g(x) = | x + 1 | 0 x 2 | |
ln(x) | x > 2 |
Decide whether g(x) is continuous at the points x=0 and x=2.
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©
CalculusQuest^{TM}
Version 1
All rights reserved---1996
William A. Bogley
Robby Robson