October 10, 2015

Homework Help: asymptotes and discontinuity 2???

Posted by ronan on Saturday, September 30, 2006 at 5:34am.

consider the function f(x) = 1/x - 1 for x not=0 and f(x) = 0 for x = 0.

decide whether f(x) has

a)one symptote and two discontinuities
b)two asymptotes and two discontinuities
c)two asymptotes and one discontinuity

I'm not sure if you mean 1/(x-1) or (1/x) - 1 here, but I'll assume you mean the second one.
You should be able to see that 1/x has one discontinuity and two asymptote, the two axis. When we subtract 1 from it to get 1/x -1, all we've done is shift the function down 1 unit, but it still has similar behavior.
Defining the function to be 0 at x-0 does not make f(x) continuous there; 0 is not a removable discontinuity for 1/x.

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