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 h(t) = 2t + 24 of the number of canisters. Which statements are true regarding the domain and range of this function? Select all that apply.

Answer 1

To analyze the function \( h(t) = 2t + 24 \), where \( t \) represents the number of canisters Wong can use (up to 10), we can determine both the domain and range.

Domain

• Wong can use anywhere from 0 up to 10 canisters.
• Therefore, the domain of \( t \) is \( [0, 10] \).

Range

• Now, we can find the minimum and maximum values of \( h(t) \) within the domain:

  • When \( t = 0 \): \[ h(0) = 2(0) + 24 = 24 \]
  • When \( t = 10 \): \[ h(10) = 2(10) + 24 = 20 + 24 = 44 \]

• Thus, as \( t \) varies from 0 to 10, \( h(t) \) varies from 24 to 44.

• Therefore, the range of \( h(t) \) is \( [24, 44] \).

Summary of True Statements

1. The domain of \( h(t) \) is \( [0, 10] \).
2. The range of \( h(t) \) is \( [24, 44] \).

Any statement that accurately reflects these conclusions about the domain and range would be considered true.