Use Bisection Method for the function $f(x)=-1, x < 0, f(x) = 1, x \geq 1$ to find value of convergence

Question

We are given the function $$ \begin{cases} f(x) = -1 & x < 0 \\ f(x) = 1 & x \geq 0 \end{cases} $$

Using the Bisection Method with starting values $a=-1, b=2$, we're asked to find toward which value we converge.

Answer 1

We find $c= \frac{a+b}{2} = 0.5 $. $f(0.5)= 1 $. We let $b= c = 0.5$. Thus $c=\frac{a+b}{2}= -0.25$. We let $a=c=-0.25$. We find again $c= \frac{a+b}{2}= 0.125$. We let $b= 0.125$. As we repeat this method infinitely many times, it should thus become clear that we converge toward $0$, which is our answer.