To analyze the function described, we note the following:
- Wong can use up to 10 canisters, which means he can choose to use anywhere from 0 to 10 canisters.
- He places exactly 3 tennis balls in each canister.
Domain: The domain of the function reflects the number of canisters Wong can use. Since the number of canisters can be any whole number from 0 to 10, the correct statement regarding the domain is:
- B. The domain of the function is all whole numbers from 0 to 10.
Range: Since Wong places 3 tennis balls in each canister, the total number of tennis balls \( T \) he places can be calculated as: \[ T = 3 \times \text{(number of canisters)} \] If \( c \) is the number of canisters used, then:
- If 0 canisters are used, \( T = 3 \times 0 = 0 \)
- If 1 canister is used, \( T = 3 \times 1 = 3 \)
- If 2 canisters are used, \( T = 3 \times 2 = 6 \)
- ...
- If 10 canisters are used, \( T = 3 \times 10 = 30 \)
Thus, the total number of tennis balls \( T \) can be: \[ T = 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 \]
These values represent all multiples of 3 from 0 to 30. The correct statement regarding the range is:
- D. The range of the function is all multiples of 3 from 0 to 30.
Final True Statements:
- 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.
2 answers