Final answer:
Multiples of the function f(x) = c/x represent inverse variation. For continuous probability functions, we calculate the area under the probability density function to determine probabilities between intervals. For a constant probability function f(x) = 12 restricted to 0 ≤ x ≤ 12, P(0 < x < 12) is 1.
Step-by-step explanation:
The multiples of the partial function f(x) = \frac{c}{x}, where c is a nonzero real number, are essentially values of the function at different points of x. Since the product of f(x) multiplied by x must equal the constant c, when f(x) is small, x must be large to maintain the equation, and vice versa. This is a fundamental property of an inverse variation function like f(x).
When discussing continuous probability functions and the cumulative distribution function (cdf), we are dealing with a different kind of function. The cdf is represented as P (X \leq x) and calculates the probability that a random variable X will take a value less than or equal to x. Related to this is the concept that the probability P of a continuous random variable taking on any single individual value is zero because there is no area under the density function at a single point.
To find the probability P(0 < x < 12) for a continuous probability function f(x) = 12, where the function is restricted to 0 \leq x \leq 12, you would calculate the area under the curve of f(x) between 0 and 12. Since f(x) is a constant function in this interval, the area under the curve is simply the product of the width (12 - 0) and the height (12), which equals 144, representing a probability of 1.