1. **Problem Statement:** We need to define a piecewise function $f(x)$ representing the cost of electricity for up to 700 units, where the cost per unit changes based on the number of units consumed. 2. **Given Rates:** - For $x \leq 100$, cost per unit = 5 - For $100 < x \leq 200$, cost per unit = 20 - For $200 < x \leq 300$, cost per unit = 40 - For $300 < x \leq 400$, cost per unit = 60 - For $400 < x \leq 500$, cost per unit = 80 - For $500 < x \leq 600$, cost per unit = 100 - For $600 < x \leq 700$, cost per unit = 150 - For $x > 700$, cost per unit = 300 (not needed as per problem) 3. **Constructing the piecewise function $f(x)$:** We calculate the cost cumulatively for each interval: $$ f(x) = \begin{cases} 5x & 0 \leq x \leq 100 \\ 5 \times 100 + 20(x - 100) & 100 < x \leq 200 \\ 5 \times 100 + 20 \times 100 + 40(x - 200) & 200 < x \leq 300 \\ 5 \times 100 + 20 \times 100 + 40 \times 100 + 60(x - 300) & 300 < x \leq 400 \\ 5 \times 100 + 20 \times 100 + 40 \times 100 + 60 \times 100 + 80(x - 400) & 400 < x \leq 500 \\ 5 \times 100 + 20 \times 100 + 40 \times 100 + 60 \times 100 + 80 \times 100 + 100(x - 500) & 500 < x \leq 600 \\ 5 \times 100 + 20 \times 100 + 40 \times 100 + 60 \times 100 + 80 \times 100 + 100 \times 100 + 150(x - 600) & 600 < x \leq 700 \end{cases} $$ 4. **Simplify constants:** - $5 \times 100 = 500$ - $20 \times 100 = 2000$ - $40 \times 100 = 4000$ - $60 \times 100 = 6000$ - $80 \times 100 = 8000$ - $100 \times 100 = 10000$ So, $$ f(x) = \begin{cases} 5x & 0 \leq x \leq 100 \\ 500 + 20(x - 100) & 100 < x \leq 200 \\ 2500 + 40(x - 200) & 200 < x \leq 300 \\ 6500 + 60(x - 300) & 300 < x \leq 400 \\ 12500 + 80(x - 400) & 400 < x \leq 500 \\ 20500 + 100(x - 500) & 500 < x \leq 600 \\ 30500 + 150(x - 600) & 600 < x \leq 700 \end{cases} $$ 5. **Example calculation:** For July units = 210, Since $200 < 210 \leq 300$, use third case: $$ f(210) = 2500 + 40(210 - 200) = 2500 + 40 \times 10 = 2500 + 400 = 2900 $$ 6. **Graph:** The graph is a piecewise linear function with breakpoints at 100, 200, 300, 400, 500, 600, and 700 units, with slopes corresponding to the unit costs in each interval.