Question

Describe any domain restrictions that make sense for each of these scenarios: The price of a stock fluctuates several times throughout the year as a function of time. A ball is hit into the air by a baseball player, rises until it reaches its highest point, and then falls into left field. The volume of a spherical balloon increases as the balloon is blown up and decreases as air is let out of it.

Answer 1

Answer:

• a) Restriction: days of the year (a discrete time)

• b) The time the ball is on the air: t = 0, until the balls touchs the ground (any real value from t = 0 to t when the ball hits the ground)

• c) Any positive real value: x ≥ 0

Explanation:

The domain is the set of elements that can be inputs of the function.

1. The price of a stock fluctuates several times throughout the year as a function of time.

The input variable is the time through out the year.

If you assume that the fluctuaion is recorded once a day, and not every second, the logical assumption is that the time is a day of the year.

Thus, the restricion is the days of the year.

You could represent them in different forms, like DD/MM/YY, or even as a number from 1 to 365 if it covers just one year.

2. A ball is hit into the air by a baseball player, rises until it reaches its highest point, and then falls into left field.

The domain is the time the ball is on the air, which may be any real value from t = 0, until the balls touchs the ground.

It is not restricted to integer numbers.

3. The volume of a spherical balloon increases as the balloon is blown up and decreases as air is let out of it.

The inputs of the function are amounts of air, which may be measured as number of moles.

The number of moles can be any real value equal or greater than zero.

Thus, the domain is the positive real values x ≥ 0.

Answer 2

Answer:

A.) Time is bounded below by zero, or by whatever time the stock price begins to be tracked (the beginning of January, for example), because it doesn’t make sense to have negative time.

B.) Again, time can’t be negative, so the domain is bounded below by zero. Since the height also can’t be negative, the domain is bounded above by the time when the ball hits the ground.

C.) The radius of the balloon is bounded below, because the balloon won’t continue to get smaller once all the air is removed. The radius is also bounded above because at some point the balloon can’t be blown up any more or it will pop.

Step-by-step explanation: