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.
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.
Answers
GPT-4o mini
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.
- 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.