Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.1 Four Ways to Represent a Function - 1.1 Exercises - Page 22: 66

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 $0\leq x\leq 2000$:
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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.
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