Answer
See the graph below.
Work Step by Step
See the graph and table above in which we evaluate $f(x)$ when x is close to 0, on either side of zero.
The function can not be extended to a continuous function,
as the left-sided limit at x=0 ($\approx-2.3026)$
does not equal the right-sided limit at x=0 ($\approx+2.3026$)
If we set $f(0)\approx 2.3026$ , f will be continuous from the right.
If we set $f(0)\approx-2.3026$ , f will be continuous from the left.