Question: The table shows data collected to represent the functional relationship between the number of people attending a wedding and the cost of the wedding.
People, $x$ Cost ($), $y$
5 445
10 890
15 1,335
20 1,780
25 2,225
What is the domain of the function represented by the table?
○ all real numbers
○ $x \geq 0$
○ all integers greater than or equal to zero
○ ${5, 10, 15, 20, 25}$
1. **State the problem:** We are given a table showing the number of people attending a wedding ($x$) and the corresponding cost of the wedding ($y$). We need to determine the domain of the function represented by this table.
2. **Understand the domain:** The domain of a function is the set of all possible input values ($x$) for which the function is defined.
3. **Analyze the table:** The table lists specific values of $x$: 5, 10, 15, 20, and 25. These are discrete values, not a continuous range.
4. **Interpret the options:**
- "all real numbers" means any number including decimals and fractions, which is not supported by the table.
- "$x \geq 0$" means all non-negative real numbers, which is also not supported since the table only shows specific values.
- "all integers greater than or equal to zero" means all whole numbers starting from 0, but the table only shows some multiples of 5.
- "${5, 10, 15, 20, 25}$" means exactly the values listed in the table.
5. **Conclusion:** Since the function is only defined for the specific values given in the table, the domain is the set ${5, 10, 15, 20, 25}$.
**Final answer:** The domain of the function is ${5, 10, 15, 20, 25}$.