Final answer:
The average rate of change of the function g(x) = 2x - 2 between the points (-1, -4) and (4, 6) is calculated as the slope of the line joining the points and is found to be 2.
Step-by-step explanation:
The question pertains to finding the average rate of change of a function between two points, which in mathematical terms means calculating the slope of the line that joins these points. For the linear function g(x) = 2x - 2, the average rate of change between points (-1, -4) and (4, 6) is found as follows:
- Identify the coordinates of the two points: Point 1 (-1, -4) and Point 2 (4, 6).
- Use the slope formula, which is the change in y divided by the change in x (sometimes referred to as rise over run).
- Substitute the coordinate values into the slope formula: Slope = ∆y / ∆x = (6 - (-4)) / (4 - (-1)) = 10 / 5 = 2.
This calculation shows that the average rate of change of g(x) between the points given is 2.
It's important to note that for linear functions the average rate of change is constant and equal to the slope of the line, irrespective of the chosen interval.