To determine the domain of the function representing the given situation, we first need to identify feasible values for the number of students (`x`) that the art teacher can pay for with $80.
Given that each ticket costs $10 per student, and the total budget is $80, we can set up the following equation to determine the maximum number of students she can accommodate:
\[ 10x \leq 80 \]
Solving for `x`:
\[ x \leq \frac{80}{10} \]
\[ x \leq 8 \]
This means that the maximum number of students she can take is 8.
Since the number of students (`x`) must be a whole number (you can't have a fraction of a student going to the museum), the possible values for `x` range from 0 to 8.
Thus, the domain of the function is the set of all integers from 0 to 8 inclusive. Mathematically, we can represent this set as:
\[ \{0, 1, 2, 3, 4, 5, 6, 7, 8\} \]
In summary, the domain of the function, which represents the number of students that can go to the museum given the budget constraints, is:
\[ \boxed{\{0, 1, 2, 3, 4, 5, 6, 7, 8\}} \]
An art teacher has $80 to spend on museum tickets for her students. Admission tickets cost $10 per student. The graph shows the linear relationship between `y`, the amount of money remaining for tickets, and `x`, the number of students going to the museum.
The art teacher plans to spend all of the money on admission tickets. Which set best represents the domain of the function for this situation?
1 answer