A coach has `72` tennis balls for the school's tennis team. The coach will give each player `6` tennis balls. The graph shows the linear relationship between `y`, the number of tennis balls remaining for the team, and `x`, the number of players on the team.
The coach will use no more than `8` players on the school's tennis team. Which set best represents the range of the function for this situation?
Since each player receives `6` tennis balls, the number of tennis balls used is equal to `6x` (where `x` is the number of players). Therefore, the number of tennis balls remaining is given by:
y = 72 - 6x
To find the range of the function, we need to determine the largest and smallest possible values of `y` for `x` between `1` and `8` (since the coach is using no more than `8` players). We can do this by plugging in the values of `x` into the equation and calculating `y`:
When x = 1:
y = 72 - 6(1) = 66
When x = 8:
y = 72 - 6(8) = 24
Therefore, the range of the function is from `24` to `66`. The set that best represents this range is {y | 24 ≤ y ≤ 66}.
To determine the range of the function, we need to find the possible values of `y`, the number of tennis balls remaining for the team.
Given that the coach has 72 tennis balls and each player receives 6 tennis balls, we can find the number of tennis balls remaining using the equation `y = 72 - 6x`, where `x` represents the number of players on the team.
Since the coach will use no more than 8 players on the team, we can substitute values of `x` from 1 to 8 into the equation and calculate the corresponding values of `y`.
For `x = 1`, `y = 72 - 6(1) = 66`.
For `x = 2`, `y = 72 - 6(2) = 60`.
For `x = 3`, `y = 72 - 6(3) = 54`.
For `x = 4`, `y = 72 - 6(4) = 48`.
For `x = 5`, `y = 72 - 6(5) = 42`.
For `x = 6`, `y = 72 - 6(6) = 36`.
For `x = 7`, `y = 72 - 6(7) = 30`.
For `x = 8`, `y = 72 - 6(8) = 24`.
Therefore, the range of the function is `{24, 30, 36, 42, 48, 54, 60, 66}`.
So, the set that best represents the range of the function for this situation is `{24, 30, 36, 42, 48, 54, 60, 66}`.