Final answer:
The function f(x)=500x-10,000 describes the elevation in feet as a function of another quantity, likely horizontal distance traveled, within a certain domain. It is a linear relationship with a slope of 500 and a y-intercept of -10,000, used to model elevation changes.
Step-by-step explanation:
The function f(x)=500x−10,000 represents a mathematical relationship used to model the elevation in feet, based on a certain input value x. In economic models, a function describes a relationship or definition, representing how one quantity varies with another.
In this context, the function likely represents the changing elevation as one moves along a certain path, where x could represent the horizontal distance traveled and f(x) the elevation above sea level at that distance.
This linear function implies that, for every unit increase in x, the elevation increases by 500 feet, minus an initial offset of 10,000 feet, within the domain of 0 ≤ x ≤ 20. It's essential to understand that the slope of the line, denoted by m in slope-intercept form, indicates how steep the line is, which in this case, is 500.