Multiple Select Question

Question

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.

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.

E.
The range of the function is all whole numbers from 0 to 30.

Answer 1

To analyze the function defined by the number of canisters and the number of tennis balls, we can summarize the situation as follows:

• Let \( x \) be the number of canisters used, where \( x \) can take any value from 0 to 10, inclusive.
• The number of tennis balls placed into the canisters is given by the function \( f(x) = 3x \).

Now we can evaluate the statements:

Domain:

1. The domain refers to the permissible values of \( x \).
2. Wong can use anywhere from 0 to 10 canisters, so:

• A. False. The domain is not all real numbers; it's restricted to whole numbers.
• B. True. The domain is all whole numbers from 0 to 10 (0, 1, 2, ..., 10).
• C. False. The domain does not extend to all whole numbers from 0 to 30; it is limited to 0 to 10.

Range:

1. The range refers to the possible outputs of the function \( f(x) \).
2. As \( x \) goes from 0 to 10, \( f(x) \) will go from \( f(0) = 0 \) to \( f(10) = 30 \), specifically taking values \( 0, 3, 6, \ldots, 30 \).
3. This means the output values will be multiples of 3 that correspond to the value of \( x \):

• D. True. The range is indeed all multiples of 3 from 0 to 30 (0, 3, 6, ..., 30).
• E. False. The range is not all whole numbers from 0 to 30; it is only the multiples of 3 in that interval.

So, the correct answers are: B and D.