1. **Problem Statement:** We need to define the piecewise function $E(d)$ that represents the down payment based on the number of units enrolled by a student. The units are integers. 2. **Given Information:** - For units from 1 to 9, down payment is 5000. - For units from 10 to 15, down payment is 10000. - For units from 16 to 21, down payment is 15000. 3. **Piecewise Function Definition:** The function $E(d)$ can be written as: $$ E(d) = \begin{cases} 5000 & \text{if } 1 \leq d \leq 9 \\ 10000 & \text{if } 10 \leq d \leq 15 \\ 15000 & \text{if } 16 \leq d \leq 21 \end{cases} $$ 4. **Explanation:** - The function assigns a fixed down payment based on the integer value of $d$ (units). - The intervals are inclusive because the problem states "from 1 to 9", etc. 5. **Answer:** The correct multiline function that defines $E(d)$ is the one matching the above piecewise definition. Since the question asks to select one option and the problem statement matches the function with intervals $1 \leq d \leq 9$, $10 \leq d \leq 15$, and $16 \leq d \leq 21$ with corresponding payments 5000, 10000, and 15000, the correct choice is option **5c**. **Final answer:** $E(d) = \begin{cases}5000 & 1 \leq d \leq 9 \\ 10000 & 10 \leq d \leq 15 \\ 15000 & 16 \leq d \leq 21 \end{cases}$