Determine the Domain of a Function: Analyzing Pool Filling Dynamics

Determine the domain of the function described below:

The function represents the amount of water in a pool while it is being filled.

To determine the domain of the function representing the amount of water in a pool while it is being filled, we should consider the nature of the process. When a pool is being filled, water is continually added over time, which implies an increase in volume.

Step-by-step solution:

• Step 1: Recognize the process described, i.e., filling a pool. This immediately suggests that the amount of water is increasing over time.
• Step 2: Understand that because water is constantly being added, the function describing the water level is always increasing.
• Step 3: Conclude that there can be no intervals where the water level decreases or remains constant, given the specific context of the process.
• Step 4: Therefore, the domain corresponds with the interval in which the function is increasing.

This analysis supports the conclusion that the nature of this function is such that it is always increasing. This matches the scenario provided, as a pool being filled with water will see its water volume continuously rise.

Thus, the correct answer is the first choice: $\text{Always increasing}$.