Final answer:
The average rate of change for a function is similar to the average velocity and is calculated using the slope of the secant line between two points on the function's graph. However, the question appears to have a typo or error, as it does not provide distinct points for calculation. Additional unrelated context from other subjects adds to the confusion but is not directly relevant to answering the mathematical query.
Step-by-step explanation:
The question asks to find the average rate of change for a given function f(x) between two points on the x-axis. The average rate of change in the context of a function is analogous to the average velocity in physics. In physics, average velocity is the total displacement (change in position, Δx) divided by the time taken (Δt), which is the slope of the displacement-time graph. When the initial time (t0) is set to zero, the average velocity can be simplified to a function of displacement and time.
To calculate the average rate of change of a function f(x) over an interval from x1 to x2, you would use the formula (f(x2) - f(x1))/(x2 - x1), which is the slope of the secant line connecting the two points on the graph of the function. However, the provided information seems to be unclear or misstated, as it repeats 'x and x' without specifying different values for the x-coordinates, making it impossible to calculate the average rate of change. Furthermore, additional context from the subjects of probability and chemistry are mentioned but do not pertain directly to the question of average rate of change in a mathematical function.