Let

$$f(x)= \begin{cases}2-x, & 0 \leq x<1 \\ k, & x=1 \\ 2x-1, & 1<x \leq 2\end{cases}$$

then:
a. What are domain and range of $f(x)$?
b. Find the value of $k$ for which $f(x)$ is continuous at $x=1$.
c. State value of $x$ where only left-hand limit and only right-hand limit exist.
d. Sketch the graph of $f(x)$.