Answer: Step-by-step explanation:
To find the average rate of change of a function over an interval, we can use the following formula:
average rate of change = (y2 - y1)/(x2 - x1)
Where x1 and x2 are the values of x at the beginning and end of the interval, and y1 and y2 are the corresponding values of the function at those points.
In this case, we are asked to compare the average rate of change of the functions g(x) and f(x) over the interval where -1≤x≤3.
For the function g(x) = x²+6x, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:
average rate of change = (g(3) - g(-1))/(3 - (-1))
= (9 + 18 - (1 - 6))/(4)
= 27/4
= 6.75
For the function f(x) = 2, we can plug in the given values for x1, x2, y1, and y2 to find the average rate of change:
average rate of change = (f(3) - f(-1))/(3 - (-1))
= (2 - 2)/(4)
= 0
Since the average rate of change of the function g(x) is greater than the average rate of change of the function f(x), the function g(x) has a greater average rate of change over the interval where -1≤x≤3.
I hope this helps clarify the comparison of the average rate of change for these two functions. Do you have any other questions?