limits - What is the breakpoint of a piecewise function?

For

$$
f(x)=\left\{\begin{matrix}
0, & x\leq -1\\
\sqrt{1-x^2},& -1 < x < 1 \\
x, & x\geq 1
\end{matrix}\right.
$$

My book says that the breakpoints are x = -1 and x = 1. How breakpoints are defined so that -1 and 1 is chosen?