Point of Discontinuity for y=|x|/x: Is it x=0?

[grace77]

Suppose y=|x|/x

I know it is a jump discontinuity but how is the point of discontinuity x=0??

 

[lurflurf]

$$\lim_{x\rightarrow 0^-}\frac{| x |}{x} \ne \lim_{x\rightarrow 0^+}\frac{| x |}{x}$$

 

[Mark44]

Suppose y=|x|/x

I know it is a jump discontinuity but how is the point of discontinuity x=0??
View attachment 66595

Your graph clearly shows that this function is discontinuous at x = 0.

 

[DrewD]

Suppose y=|x|/x

I know it is a jump discontinuity but how is the point of discontinuity x=0??
View attachment 66595

What bothers you about that? Do you think the discontinuity should be somewhere else? Are you bothered about $\frac00$? Answers to these might help uncover your misconception.