An apartment building has a total of 120 apartments. The equation \( m(p)=5 p \) gives the amount of money made, in hundreds of dollars, when \( p \) apartments are rented. What is the domain for this situation? \( \{m(p) \mid m(p) \leq 600\} \) \( \left\{\begin{array}{|l|}\hline \square\{0,1,2,3, \ldots 120\}\end{array}\right. \) \( \{0,5,10,15,20, \ldots, 600\} \)

To determine the **domain** for the function \( m(p) = 5p \), where \( p \) represents the number of apartments rented in a building with a total of 120 apartments, consider the following: 1. **Possible Values of \( p \):** - \( p \) must be an integer because you can't rent a fraction of an apartment. - \( p \) can range from 0 (no apartments rented) to 120 (all apartments rented). 2. **Interpreting the Options:** - **Option 1:** \( \{m(p) \mid m(p) \leq 600\} \) This describes the **range** of the function (possible values of \( m(p) \)), not the domain. - **Option 2:** \( \{0, 1, 2, 3, \ldots, 120\} \) This correctly represents the **domain** of \( p \), specifying all possible integer values from 0 to 120. - **Option 3:** \( \{0, 5, 10, 15, 20, \ldots, 600\} \) This also describes the **range** of the function \( m(p) \), as it lists the possible outputs based on the domain. **Conclusion:** The correct domain is the set of integers from 0 to 120, which is represented by the second option. **Answer:** \( \{0,1,2,3, \ldots, 120\} \)