To analyze the function described, we note that the number of tennis balls Wong places into canisters depends on the number of canisters he has available to use. Since Wong can use up to 10 canisters and he places exactly 3 tennis balls in each canister, we can express the function mathematically as:
\[ B(c) = 3c \]
where \( B \) is the total number of tennis balls and \( c \) is the number of canisters.
Now let's determine the domain and range:
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Domain: The domain represents all possible values of the input variable, which in this case is the number of canisters \( c \). Since he can use anywhere from 0 to 10 canisters, the domain is: \[ 0 \leq c \leq 10 \]
Therefore, the domain consists of all integer values from 0 to 10 (inclusive).
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Range: The range represents all possible outputs of the function, which in this case is the total number of tennis balls \( B(c) \). For \( c = 0 \): \[ B(0) = 3 \times 0 = 0 \] For \( c = 1 \): \[ B(1) = 3 \times 1 = 3 \] For \( c = 10 \): \[ B(10) = 3 \times 10 = 30 \]
Thus, the range includes the outputs starting from 0 (when no canisters are used) and increases in increments of 3 up to 30 (when all 10 canisters are filled). The possible values (0, 3, 6, 9, ..., 30) can be expressed as: \[ 0 \leq B(c) \leq 30 \] This range consists of all multiples of 3 from 0 to 30.
Based on this evaluation, the following statements about the domain and range can be considered true:
- The domain is \( [0, 10] \) (can include both 0 and 10).
- The range consists of all multiples of 3 from 0 to 30: \( {0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30} \).
You may need to select statements regarding the domain and range based on the above information.