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continuity
- Thread starter thepie
- Start date
D
Deleted member 4993
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thepie said:Find the x values (if any) at which f is not continuous. Is this discontinuity removable?
f(x)= Ix-3I/x-3
Investigate the behaviour of the function as you approach x = 3 - from the left and from the right. Use your graphing calculator.
Please share with us your work/thoughts, indicating exactly where you are stuck - so that we know where to begin to help you
D
Deleted member 4993
Guest
thepie said:I'm not suppose to use my calculator, and I'm not sure how to start the problem.
Then plot it by hand - that's not too difficult...
BigGlenntheHeavy
Senior Member
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- Mar 8, 2009
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\(\displaystyle f(x) \ = \ \frac{|x-3|}{x-3}.\)
\(\displaystyle If \ x \ is \ greater \ than \ three, \ then \ f(x) \ = \ 1.\)
\(\displaystyle If \ x \ is \ less \ than \ three, \ then \ f(x) \ = \ -1.\)
\(\displaystyle If \ x \ = \ three, \ then \ f(x) \ is \ undefined; \ the \ discontinuity \ is \ nonremovable.\)
\(\displaystyle If \ x \ is \ greater \ than \ three, \ then \ f(x) \ = \ 1.\)
\(\displaystyle If \ x \ is \ less \ than \ three, \ then \ f(x) \ = \ -1.\)
\(\displaystyle If \ x \ = \ three, \ then \ f(x) \ is \ undefined; \ the \ discontinuity \ is \ nonremovable.\)