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I have a problem with the two last questions of this exercise.

1) At which points is the absolute value function f(x) = |x| continuous?

$\forall x \in \mathbb{R}$ f is continuous

2) What about $f(x)=\frac{|x|}{x}$

$\forall x \in \mathbb{R}-{0}$, f is continuous

3) And what about $f(x)=\begin{cases} \frac{|x|}{x} &\text{if }x \neq 0\\0 &\text{if }x=0\end{cases}$

4) What type of discontinuities appear if any at all?

Thank you in advance

2 Answers 2