MARKIN BRAINIEST!!! PLZ HELP!!!Over the interval (1,2),(3,4),(4,5),(2,3), the average rate of change of g is greater than the average rate of change of f.As the value of x increases, the average rates of change of f and g (remain constant decrease),(decrease and increase),(remain constant and increasing),(decrease and decrease),(increase and decrease),(increase and increase) , respectively.When the value of x is equal to 8, the value of (f(x) equals the value of g(x)),(g(x) exceeds value of f(x),(f(x) exceeds value of g(x)It can be further generalized that a quantity increasing exponentially will (always),(eventually),(never) exceed a quantity increasing linearly.

Answer:(4, 5)remain constant and increaseg(x) exceeds the value of f(x)eventuallyStep-by-step explanation:a) The slope of the curve g(x) roughly matches that of f(x) at about x=4. Above that point, the curve g(x) is steeper than f(x), so its average rate of change will exceed that of f(x). An appropriate choice of interval is (4, 5).__b) As x increases, the slope of f(x) remains constant (equal to 4). The slope of g(x) keeps increasing as x increases. An appropriate choice of rate of change descriptors is (remain constant and increase).__c) The curves are not shown in the problem statement for x = 8. The graph below shows that g(x) has already exceeded f(x) by x=7. It remains higher than f(x) for all values of x more than that. We can also evaluate the functions to see which is greater:   f(8) = 4·8 +3 = 35   g(8) = (5/3)^8 ≈ 59.54 . . . . this is greater than 35   g(8) > f(8)__d) Realizing that an exponential function with a base greater than 1 will have increasing slope throughout its domain, it seems reasonable to speculate that it will always eventually exceed any linear function (or any polynomial function, for that matter).