Answer
f is not continuous on its domain.
Work Step by Step
The function f is said to be continuous on its domain if it is continuous at each point in its domain. A discontinuity can occur at $x=a$ if either
a. $\displaystyle \lim_{\mathrm{x}\rightarrow a}f(x)$ does not exist, or
b. $\displaystyle \lim_{\mathrm{x}\rightarrow a}f(x)$ exists but is not equal to $f(a)$.
At endpoints of the domain (if any), we observe the existence of the left or right limit, as appropriate.
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At x=0, we have a discontinuity (type (a) )
because the left limit at x=0 is -1, while the right limit is +2.
Since they are not equal, the limit $\displaystyle \lim_{\mathrm{x}\rightarrow 0}f(x)$ does not exist.
f is not continuous on its domain.
