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.

No one has answered this question yet.

Answer this Question

Related Questions

calculus please help! - Which of the following functions f has a removable ...
infinite discontinuity - How do check the graph of a function has an infinite ...
Calculus - Suppose g(x) = { 1 / (x - 2) if x < 1 2x - 4 if x >/= 1...
Calculus (Discontinuity) - Suppose f(x) = [sin(x^2 - 4)]^ -1. Identify any ...
calculus - give an example of a function that has: a) only one point of ...
Calculus (Discontinuities) - Suppose, f(x) = { (x - 1)^2 / x + 1 if x < 2...
Pre Cal - which of the following best describes the behavior of thre function f(...
PreCalc - Consider the function(7+15x^2)/(10x^2+9x+10). Find the function's ...
algebra - Find the points of discontinuity and any holes. y=x^2-1/(x^2+3x+2) ...
math-calc - Consider the function f(x)= (2x+8)/(6x+3). For this function there ...

For Further Reading

First Name:
School Subject:
Answer: