Using Verbal Descriptions to Create Graphs of Functions

4.9.5 Using Verbal Descriptions to Create Graphs of Functions

4.9.5 • Using Verbal Descriptions to Create Graphs of Functions

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To prepare for a backyard party, a parent uses two identical hoses to fill a small pool that is 15 inches deep and a large pool that is 27 inches deep.

The height of the water in each pool is a function of time since the water is turned on.

A woman is filling a large above-ground pool with a hose, while a smaller inflatable kiddie pool with stars is nearby, also filling with water on a grassy area.

Here are descriptions of three situations. For each situation, sketch the graphs of the two functions on the same coordinate plane, so that $S (t)$ is the height of the water in the small pool after $t$ minutes, and $L (t)$ is the height of the water in the large pool after $t$ minutes.

In both functions, the height of the water is measured in inches.

Situation 1: Each hose fills one pool at a constant rate. When the small pool is full, the water for that hose is shut off. The other hose keeps filling the larger pool until it is full.

Sketch your interpretation of the graph of situation 1.

Compare your answer:

Line graph showing height in inches vs. time in minutes for large and small pools. The small pool levels off at 15 inches after 6 minutes, while the large pool reaches 27 inches after 16 minutes.

Situation 2: Each hose fills one pool at a constant rate. When the small pool is full, both hoses are shut off.

Sketch your interpretation of the graph of situation 2.

Compare your answer:

A graph showing water height over time in two pools. The small pools water rises quickly to 9 inches by 6 minutes, then levels off. The large pool rises to 15 inches by 6 minutes and stays constant. Axes: height in inches, time in minutes.

Situation 3: Each hose fills one pool at a constant rate. When the small pool is full, both hoses are used to fill the large pool until it is full.

Sketch your interpretation of the graph of situation 3.

Compare your answer:

Line graph showing water height (in inches) over time (in minutes) for a large pool and a small pool. Both rise quickly at first; the small pool stops at 15 inches, while the large pool rises to 27 inches.