Answer
(a)
$E(x) = \left\{
\begin{array}{ll}
10+0.06x & \quad 0\leq x \leq 1200 \\
82+(x-1200)\times0.07 & \quad x > 1200
\end{array}
\right. $
(b) See image
Work Step by Step
(a) As mentioned in the problem, $\$10$ is a base fee per month and customers pay an additional amount of money according to electricity usage, which is $\$0.06$ per kWh up to $1200 kWh$ and $\$0.07$ per kWh after $1200 kWh$.
$E(x) = \left\{
\begin{array}{ll}
10+0.06x & \quad 0\leq x \leq 1200 \\
(10+0.06\times1200)+(x-1200)\times0.07 & \quad x > 1200
\end{array}
\right. $ $=\left\{
\begin{array}{ll}
10+0.06x &\quad 0\leq x\leq 1200 \\
82+(x-1200)\times0.07 &\quad x >1200
\end{array}
\right.$
(b) See image
