To analyze the function regarding the number of canisters Wong can use and the corresponding number of tennis balls, we can define the function based on the number of canisters \( x \) and the total number of tennis balls \( y \) as follows:
\[ y = 3x, \] where \( x \) can take on any whole number value from 0 to 10 (inclusive).
Let's assess each statement about the domain and range:
A. The domain of the function is all real numbers from 0 to 10.
- This statement is false because the domain consists only of whole numbers (0, 1, 2, ..., 10), not all real numbers.
B. The domain of the function is all whole numbers from 0 to 10.
- This statement is true. The domain indeed is the whole numbers from 0 to 10, which correspond to the number of canisters Wong can use.
C. The domain of the function is all whole numbers from 0 to 30.
- This statement is false. The number of canisters is constrained to a maximum of 10, so the domain cannot extend to 30.
D. The range of the function is all multiples of 3 from 0 to 30.
- This statement is true. The possible outputs (number of tennis balls) when \( x \) takes values from 0 to 10 will be \( 3 \cdot 0, 3 \cdot 1, 3 \cdot 2, \ldots, 3 \cdot 10 \), which are 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30 — all of which are multiples of 3.
E. The range of the function is all whole numbers from 0 to 30.
- This statement is false. The outputs are specifically the multiples of 3 between 0 and 30, not all whole numbers in that range.
Thus, the true statements regarding the domain and range of this 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.
2 answers