Answer
a. Domain $(-\infty,\infty)$, Range $[-1,1]$
b. $(-\infty,-1)\cup(-1,1)\cup(1,\infty)$
c. Does not exist.
d. Does not exist.
Work Step by Step
We are given the piecewise function:
$f(x)=\begin{cases} x\hspace1cm -1\leq x\lt0, 0\lt x\leq1 \\ 1\hspace1cm x=0 \\0\hspace1cm x\lt-1, x\gt1 \end{cases}$,
We can graph the function as shown.
a. Domain $(-\infty,\infty)$, Range $[-1,1]$
b. $\lim_{x\to c}f(x)$ exist for all points except $c\ne\pm1$, in other notation $c\in(-\infty,-1)\cup(-1,1)\cup(1,\infty)$
c. For the left-hand limit only, we can not identify any points.
d. For the right-hand limit only, we can not identify any points.
