Answer
$(a)$
$E(x)=\left\{\begin{array}{ll} 0.1x+6 & \quad if & \quad 0\leq x\leq300 \\ 0.06(x-300)+36 & \quad if & \quad x\gt300 \end{array} \right. $
$(b)$ See the image below.
Work Step by Step
$(a)$
Let $E(x)$ be the cost in dollars. The cost for usage less than $300kWh$ would be $0.1x$ plus $\$6$ base rate.
For exactly $300kWh$ we have $\$30+\$6=\$36$
Any amount, more than $300$, that is $(x-300)$ is charged $\$0.06$. So for electricity more than $300$ we have $0.06(x-300) + \$36$
According to the information given, we can write:
$E(x)=\left\{\begin{array}{ll} 0.1x+6 & \quad if & \quad 0\leq x\leq300 \\ 0.06(x-300)+36 & \quad if & \quad x\gt300 \end{array} \right. $
$(b)$ See the image above.
