Final answer:
The domain of a function is all the potential input values, with the particular function in question having a domain of real numbers between 0 and 20, inclusive.
For continuous probability functions, the probability of a specific value is zero, and probabilities are calculated as the area under the curve over the interval.
Step-by-step explanation:
The domain of a function describes all the possible values that can be input into the function. For a function f(x) defined by the information given, the domain would be the set of all real numbers x with the restrictions provided. Specifically, since the function is described for 0 ≤ x ≤ 20, the domain is the closed interval from 0 to 20, inclusive.
In the context of a continuous probability function f(x), when we're asked to find the probability of an event such as P(x > 3), we look at the integral of the function over the interval from 3 to the upper limit of the domain. If the function f(x) is restricted between 1 and 4, P(x > 3) would be the area under f(x) from x equals 3 to x equals 4.
For a probability function f(x), if we want to calculate P(x = a specific value), such as P(x = 15), the probability is 0 because a precise value on a continuous distribution has zero width, hence no area under the curve.
Regarding the concept of domain in a real-world application, if we have a scenario where the horizontal velocity of a ball is graphed, and it's constant from t = 0 until t = 0.7 sec, the domain would be all real numbers between 0 and 0.7, inclusive.