What is the average rate of change of g(x)=2x-3 between the points (-2, -7) and (3, 3)?
Rate of change of a function f(x) at any point is given by the first derivative of that point.
Since this is a linear function you should have only one rate of change at every point and it is given by the first derivative of the function.
`g(x) = 2x-3`
`g'(x) = 2`
As said earlier we have only one rate of change. It is 2.
The average rate of change is equivalent to finding the slope for linear functions. In this case slope of the function `g(x)=2x-3` is 2 since it is in slope-intercept form.
The average rate of change of g(x) from (-2,-7) to (3,3) is 2.