The problem asks us to define a function that describes the relationship between two quantities when filling a child's pool with a garden hose. We need to state the function, specifying which variable depends on the other, and consider the units of measurement. We also need to sketch a graph of the function, label the axes, and explain the meaning of a chosen point on the graph.

1. Problem Description

The problem asks us to define a function that describes the relationship between two quantities when filling a child's pool with a garden hose. We need to state the function, specifying which variable depends on the other, and consider the units of measurement. We also need to sketch a graph of the function, label the axes, and explain the meaning of a chosen point on the graph.

2. Solution Steps

a. Defining the Function:

The two quantities that are related are the time the hose is running and the volume of water in the pool. The volume of water in the pool depends on the time the hose has been running. Therefore, the volume of water is a function of the time.

We can express this as: "The volume of water in the pool (in gallons or liters) is a function of the time (in minutes or seconds) the hose has been running."

b. Sketching the Graph:

* Label the x-axis as "Time (minutes)".

* Label the y-axis as "Volume of water (gallons)".

* The graph will start at the origin (0,0), because at time 0, the pool is empty.

* As time increases, the volume of water increases. If the water flows at a constant rate, the graph will be a straight line with a positive slope. Otherwise, if the water flow is variable, the graph may be curved, but it should still be increasing.

* Draw a straight line that starts at (0,0) and increases linearly. Assume that the water flow is constant.

c. Identifying a Point on the Graph:

Let's say after 5 minutes, there are 10 gallons of water in the pool. This means the point (5, 10) is on the graph.

The meaning of the point (5, 10) is that after the garden hose has been running for 5 minutes, the volume of water in the pool is 10 gallons.

3. Final Answer

a. The volume of water in the pool (in gallons) is a function of the time (in minutes) the hose has been running.

b. The graph is a straight line starting from (0,0) with x-axis labeled "Time (minutes)" and y-axis labeled "Volume of water (gallons)".

c. The point (5, 10) on the graph means that after the garden hose has been running for 5 minutes, the volume of water in the pool is 10 gallons.