Let's analyze the situation step by step.
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Domain of the function: The domain is defined by the number of canisters Wong can use. Wong can use anywhere from 0 to 10 canisters. Therefore, the valid values for the number of canisters (the independent variable) are whole numbers from 0 to 10.
- Statement A: False - The domain is not all real numbers, it's restricted to whole numbers.
- Statement B: True - The domain consists of whole numbers from 0 to 10: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
- Statement C: False - The domain does not include all whole numbers from 0 to 30; it only goes up to 10.
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Range of the function: The range is defined by the number of tennis balls placed into canisters. If Wong places 3 tennis balls in each canister, then for any number of canisters \( n \) (where \( n \) is in the domain of 0 to 10), the total number of tennis balls is given by \( 3n \).
- If \( n = 0 \): 0 tennis balls
- If \( n = 1 \): 3 tennis balls
- If \( n = 2 \): 6 tennis balls
- If \( n = 3 \): 9 tennis balls
- If \( n = 4 \): 12 tennis balls
- If \( n = 5 \): 15 tennis balls
- If \( n = 6 \): 18 tennis balls
- If \( n = 7 \): 21 tennis balls
- If \( n = 8 \): 24 tennis balls
- If \( n = 9 \): 27 tennis balls
- If \( n = 10 \): 30 tennis balls
The possible values for the total number of tennis balls are {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30}, which are all multiples of 3 between 0 and 30.
- Statement D: True - The range includes all multiples of 3 from 0 to 30.
- Statement E: False - The range does not include all whole numbers from 0 to 30, but only specific multiples of 3.
Thus, the correct statements regarding the domain and range are:
- B. The domain of the function is all whole numbers from 0 to 10.
- D. The range of the function is all multiples of 3 from 0 to 30.
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