Is it correct to say that $f(t)$ is bounded and piecewise continuous with discontinuities at $t = \pm 2, \pm 6, ...$?

Question

I have the function

$$ f(t) = \begin{cases} -t & \text{when, }-2<t\le0,\\ t & \text{when, }0<t\le2. \end{cases} $$

and its periodic extension, $f(t + 4) = f(t)$

If I am not mistaken, we have $\lim\limits_{t \to -2^+} f(t) = 2$

and

$\lim\limits_{t \to -2^-} f(t) = \lim\limits_{t \to 2^-} f(t - 4) = -2$.

So is it correct to say that $f(t)$ is bounded and piecewise continuous with discontinuities at $t = \pm 2, \pm 6,\cdots$?

I would greatly appreciate it if people could please take the time to clarify this.