2010002109

There is a part of the function $$f(x)=\{\begin{array}{ccc}& -|x+2|+4,& x\in (-\mathrm{\infty };1)\setminus \{-3\}\\ & 1,& x\in [1;2)\\ & 2,& x\in [2;5]\\ & 3-(x-6{)}^{-2}& x\in (5;\mathrm{\infty })\setminus \{6\}\end{array}$$ in the picture. Use the graph to determine at how many points of the given interval $[-4;8]$ is the function $f$ defined and is not differentiable.