You jumped from a high ledge into a pool of water, then swam to the other side of the pool and climbed up a ladder at a constant rate to get out of the pool. Compare your height around the surface of the pool water to the time.

Question

Identify the types of functions that can be used to describe each part of the situation described above. The second sentence above gives you the information needed to sort out which axis represents which variable.

(1 point)
The initial fall would be represented by a
because
The swim across the pool would be represented by a
because
Climbing the ladder would be represented by a
because
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Answer 1

To analyze the situation described, we can break it down into three parts: the initial fall, the swim across the pool, and the climb up the ladder. Each part can be represented using different types of mathematical functions based on their characteristics.

1. The initial fall would be represented by a quadratic function (or a parabola) because the motion of falling under the influence of gravity follows a parabolic trajectory. The height above the water decreases as time progresses until you hit the water.

2. The swim across the pool would be represented by a constant function (or a horizontal line) because your height remains constant while you swim. As you are underwater, the height above the water does not change with respect to time.

3. Climbing the ladder would be represented by a linear function because as you climb, your height above the water increases at a constant rate over time. This creates a straight line when graphing height against time, with a positive slope.

To summarize the functions that represent each part of the situation:

• The initial fall: Quadratic function
• The swim across the pool: Constant function
• Climbing the ladder: Linear function