If f(x) = |x|/x for x neq 0 and 1 for x = 0,t | vedclass

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(C) The function is defined as $f(x) = \begin{cases} 1 & x > 0 \ -1 & x < 0 \ 1 & x = 0 \end{cases}$.To check for continuity at $x = 0$,we evaluate

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neither continuous nor differentiable at $x = 0$

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(C) The function is defined as $f(x) = \begin{cases} 1 & x > 0 \ -1 & x To check for continuity at $x = 0$,we evaluate the left-hand limit and right-hand limit:$\lim_{x 	o 0^-} f(x) = -1$$\lim_{x 	o 0^+} f(x) = 1$Since the left-hand limit is not equal to the right-hand limit,the function is discontinuous at $x = 0$.Since the function is not continuous at $x = 0$,it is also not differentiable at $x = 0$.Therefore,the function is neither continuous nor differentiable at $x = 0$.

If $f(x) = |x|/x$ for $x \neq 0$ and $1$ for $x = 0$,then the function is

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