SOLUTION: Is the function f(x)=|x|/x continuous?_____ If not continuous, a) At what value of x does the discontinuity occur? b) What type of discontinuity is it c) Is it removable discon

Question 912264: Is the function f(x)=|x|/x continuous?_____
If not continuous,
a) At what value of x does the discontinuity occur?
b) What type of discontinuity is it
c) Is it removable discontinuity or not?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
by definition, |x| = x if x >= 0. If x < 0, then |x| = -x

So, |x|/x = x/x = 1 when x >= 0

However, when x < 0, then |x|/x = -x/x = -1

-------------------------------------------------------

This means

$f(x) = \frac{|x|}{x} = \begin{cases} 1 \ \mbox{if } x \ge 0 \\ -1 \ \mbox{if } x < 0 \\ \end{cases}$

So there is a discontinuity at x = 0 due to that jump from y = -1 to y = 1.

It is a jump discontinuity and it is not removable.

Graph:

Ignore that vertical piece. It's just a glitch in the graphing process.
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