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?