After tennis practice, Wong places tennis balls into canisters. He can use up to 10 canisters, and he places exactly 3 tennis balls into each canister. The number of tennis balls placed into canisters is a function of the number of canisters.

Question

Which statements are true regarding the domain and range of this function? Select all that apply.
A.
The domain of the function is all real numbers from 0 to 10.

B.
The domain of the function is all whole numbers from 0 to 10.

C.
The domain of the function is all whole numbers from 0 to 30.

D.
The range of the function is all multiples of 3 from 0 to 30.

Answer 1

To analyze the statements regarding the function Wong created for placing tennis balls into canisters, we first define the function based on the information provided. If \( n \) represents the number of canisters, then the function for the number of tennis balls \( B(n) \) can be expressed as:

\[ B(n) = 3n \]

Given that Wong can use up to 10 canisters, the possible values for \( n \) (the number of canisters) are whole numbers from 0 to 10.

Domain:

1. Statement A: The domain of the function is all real numbers from 0 to 10.

   • False. The domain is not all real numbers; it is limited to whole numbers (integer values).

2. Statement B: The domain of the function is all whole numbers from 0 to 10.

   • True. The valid values for \( n \) (the number of canisters) are 0, 1, 2, ..., up to 10.

3. Statement C: The domain of the function is all whole numbers from 0 to 30.

   • False. The number of canisters cannot exceed 10, so the domain cannot include numbers greater than 10.

Range:

To determine the range, we consider the outputs of the function based on the valid inputs:

• With \( n = 0 \): \( B(0) = 3 \times 0 = 0 \)
• With \( n = 1 \): \( B(1) = 3 \times 1 = 3 \)
• With \( n = 2 \): \( B(2) = 3 \times 2 = 6 \)
• With \( n = 3 \): \( B(3) = 3 \times 3 = 9 \)
• With \( n = 4 \): \( B(4) = 3 \times 4 = 12 \)
• With \( n = 5 \): \( B(5) = 3 \times 5 = 15 \)
• With \( n = 6 \): \( B(6) = 3 \times 6 = 18 \)
• With \( n = 7 \): \( B(7) = 3 \times 7 = 21 \)
• With \( n = 8 \): \( B(8) = 3 \times 8 = 24 \)
• With \( n = 9 \): \( B(9) = 3 \times 9 = 27 \)
• With \( n = 10 \): \( B(10) = 3 \times 10 = 30 \)

Thus, the range of \( B(n) \) based on the possible values of \( n \) is \( 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 \), which are all multiples of 3 up to 30.

4. Statement D: The range of the function is all multiples of 3 from 0 to 30.
   • True. The outputs \( B(n) \) yield all multiples of 3 from 0 to 30, inclusive.

Conclusion

The true statements regarding the domain and range of the function 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.