Answer
f is not continuous on its domain,
discontinuities at x=-1 and at x=0.
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=-1, the left and right limits equal -1,
$\displaystyle \lim_{\mathrm{x}\rightarrow-1}f(x)$=-1 exists but is not equal to $f($-1$)$=1
By case (b), a discontinuity occurs at x=-1.
Also, at x=0, f(0) is defined, f(0)=2,
but neither of the left or right limits exits as they diverge to $\pm\infty)$
By (a), a discontinuity occurs at x=0.
