a. Graph the function 0 Sxs1 12 - x, 1

We have to find out the given function is continuous and differentiable at $x=1$ or not.

Continuity at $x=1$:

Left hand limit

$\begin{array}{rcl}\underset{x\to 1^{-}}{\lim }f\left(x\right)& =& \underset{x\to 1^{-}}{\lim }\left(x\right)\\ & =& 1\\ & & \end{array}$

Right hand limit:

$\begin{array}{rcl}\underset{x\to 1^{+}}{\lim }f\left(x\right)& =& \underset{x\to 1^{+}}{\lim }\left(2-x\right)\\ & =& 1\end{array}$

Value of function at $x=1$ is $f\left(1\right)=1$

Left hand limit, right hand limit and value of function at $x=1$ are equal.

So, function is continuous at $x=1$.