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.

1 answer

To analyze the situation, we can define the function based on the number of canisters Wong uses to determine the total number of tennis balls he places in the canisters.

Let:

  • \( c \) = number of canisters Wong uses (can range from 0 to 10)
  • The function relating canisters to tennis balls is: \( f(c) = 3c \)

Domain:

  • Wong can use from 0 up to 10 canisters. Therefore, the domain of the function \( f(c) \) in this case is the count of canisters he can choose.
  • Since \( c \) must be a whole number (he can't use a fraction of a canister), the options for \( c \) are 0, 1, 2, ..., 10.

Thus, the correct statement regarding the domain is: B. The domain of the function is all whole numbers from 0 to 10.

Range:

  • The total number of tennis balls \( f(c) = 3c \) will yield the following values as \( c \) varies from 0 to 10:
    • \( f(0) = 3 \times 0 = 0 \)
    • \( f(1) = 3 \times 1 = 3 \)
    • \( f(2) = 3 \times 2 = 6 \)
    • \( f(3) = 3 \times 3 = 9 \)
    • \( f(4) = 3 \times 4 = 12 \)
    • \( f(5) = 3 \times 5 = 15 \)
    • \( f(6) = 3 \times 6 = 18 \)
    • \( f(7) = 3 \times 7 = 21 \)
    • \( f(8) = 3 \times 8 = 24 \)
    • \( f(9) = 3 \times 9 = 27 \)
    • \( f(10) = 3 \times 10 = 30 \)

These evaluate to the following outputs for the function \( f(c) \): 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. Therefore, the range consists of:

  • \( 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, 30 \)

The range can be defined as all multiples of 3 from 0 to 30.

Thus, the correct statement regarding the range is: D. The range of the function is all multiples of 3 from 0 to 30.

Summary of Selected 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.