To analyze the situation in the question, let’s break down the information given:
- Tina can use up to 10 canisters.
- She places exactly 3 tennis balls into each canister.
Domain
The domain of the function represents the possible values of canisters. Since Tina can use from 0 to 10 canisters, we can conclude:
- The domain must include all whole numbers from 0 to 10. This means the only acceptable values for the number of canisters are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10.
Therefore, the correct statement about the domain is:
- The domain of the function is all whole numbers from 0 to 10.
Range
The range of the function is determined by the number of tennis balls that can be placed into the canisters. Since each canister contains 3 tennis balls, the number of balls can be calculated as follows:
- If \( n \) is the number of canisters, then the total number of tennis balls \( B \) is given by: \[ B = 3n \]
Considering \( n \) can take the values 0 through 10:
- For \( n = 0 \), \( B = 3 \cdot 0 = 0 \)
- For \( n = 1 \), \( B = 3 \cdot 1 = 3 \)
- For \( n = 2 \), \( B = 3 \cdot 2 = 6 \)
- For \( n = 3 \), \( B = 3 \cdot 3 = 9 \)
- For \( n = 4 \), \( B = 3 \cdot 4 = 12 \)
- For \( n = 5 \), \( B = 3 \cdot 5 = 15 \)
- For \( n = 6 \), \( B = 3 \cdot 6 = 18 \)
- For \( n = 7 \), \( B = 3 \cdot 7 = 21 \)
- For \( n = 8 \), \( B = 3 \cdot 8 = 24 \)
- For \( n = 9 \), \( B = 3 \cdot 9 = 27 \)
- For \( n = 10 \), \( B = 3 \cdot 10 = 30 \)
Thus, the possible values of \( B \) are 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. This corresponds to all multiples of 3 from 0 to 30.
Thus, the relevant statements about the range are:
- The range of the function is all multiples of 3 from 0 to 30.
Conclusion
The true statements are:
- The domain of the function is all whole numbers from 0 to 10.
- The range of the function is all multiples of 3 from 0 to 30.
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