Answer
(a) $
E(x) = \left\{
\begin{array}{ll}
0.06x+10 & \quad x \leq 1200 \\
0.07x & \quad x > 1200
\end{array}
\right.
$
(b) The following is the graph of E(x) for $0\leq x\leq 2000$:
Work Step by Step
(a) For the first 1200 kWh, customers are charged 6 cents per kWh. Since the x-value in this function is the amount of electricity used, 0.06 is multiplied with x. There is also a base rate of 10 dollars, so the final function is:
$0.06x + 10$ for $x\leq1200$
For all usage over 1200 kWh per month, customers are charged 7 cents per kWh. Thus the function in the domain $x>1200$ becomes:
$0.07x $ for $x>1200$
The function E is expressed as a piecewise function.
(b) Points are plotted using the function that was found in part (a) and the points are joined together. The domain is limited to $0\leq x\leq 2000$ as per the requirements of the question.
