Let's carefully analyze the problem to determine the correct answer.
Given:
- The carwash charges [tex]$\$[/tex]8[tex]$ per car.
- The carwash can wash at most 10 cars per hour.
We need to find the domain of the relation, which is the set of all possible numbers of cars that can be washed in one hour.
Step-by-step solution:
1. Determine the maximum and minimum number of cars that can be washed in one hour:
- The minimum number of cars that can be washed in one hour is $[/tex]0[tex]$ (if no cars show up).
- The maximum number of cars that can be washed in one hour is $[/tex]10[tex]$ (as given).
2. List all possible numbers of cars that can be washed within the given range:
- These are the integers from $[/tex]0[tex]$ to $[/tex]10[tex]$ inclusive, because the carwash can wash between $[/tex]0[tex]$ and $[/tex]10[tex]$ cars per hour.
3. Identify the appropriate set that represents these numbers:
- The set of all these possible numbers is $[/tex]\{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}[tex]$.
4. Match this set with the given options to select the correct one:
- The options given are:
- A. $[/tex]\{0,1,2,3,4,5,6,7,8,9,10\}[tex]$
- B. $[/tex]\{0,8,16,24,32,40,48,56,64,72,80\}[tex]$
- C. $[/tex]0 \leq x < 80[tex]$
- D. $[/tex]0 \leq x \leq 10[tex]$
- Option A, $[/tex]\{0,1,2,3,4,5,6,7,8,9,10\}[tex]$, is exactly the set of all possible numbers of cars that can be washed in one hour.
Therefore, the correct answer is:
A. $[/tex]\{0,1,2,3,4,5,6,7,8,9,10\}$
