Final answer:
The subject of this question is Mathematics at a High School level.
Step-by-step explanation:
The question pertains to understanding continuous functions and their properties, such as continuous derivatives. In the case of the given function g(0)=-10, it is implied that g is continuous and differentiable. Considering a horizontal line as the graph of the function f(x), the function value does not change as x varies. It is also mentioned that for the continuous probability distribution, one must understand how to interpret probability values for different ranges of x.
Probability associated with a continuous probability distribution for a specified range is represented by the area under the curve of the distribution function. For instance, when considering the probability P(x > 15), if the range of x is from 0 to 15, the probability is 0 since x never goes beyond 15. Similarly, for a continuous distribution, the probability of a specific value, like P(x = 7), is always 0 because the probability of picking a single point from a continuous range is infinitesimal.
To label a graph with the function f(x), you would typically provide a consistent scale for both the x and y axes and mark the function and axis accordingly. If f(x) = 10, for 0≤x≤ 20, scale the axes up to the maximum values and draw the horizontal line at y = 10.