Increasing and Decreasing Intervals of a Function: Identifying which domain is applicable for the described function

Logically, a person's weight is something that fluctuates.

In one week, a person's weight can increase, but in the following week, it can decrease.

Therefore, the domain that suits this function is - partly increasing and partly decreasing.

According to the definition, the amount of fuel in the car's tank will always decrease, since during the trip the car consumes fuel in order to travel.

Therefore, the domain that is suitable for this function is - always decreasing.

According to logic, a child's height from birth until first grade will always be increasing as the child grows.

Therefore, the domain that suits this function is - always increasing.

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: $\text{Always increasing}$.

Logically, a person's energy level throughout the day changes and depends on many factors.

On one hand, energy levels rise for example when a person eats or consumes caffeine.

On the other hand, energy levels drop when for example a person moves a lot or exercises.

Therefore, the domain that fits this function is - partly increasing and partly decreasing.

According to logic, the computer's battery during use will always decrease since the battery serves as an energy source for the computer.

Therefore, the domain that suits this function is - always decreasing.

According to logic, the speed of the stone during a fall from a great height will increase as it falls with acceleration.

In other words, the speed of the stone increases, so the appropriate domain for this function is - always increasing.

According to logic, the student's grades throughout the year depend on many criteria that are not given to us.

Therefore, the appropriate domain for the function is - it is impossible to know.