6. given the function ( f(x)=3x^{2}-2x + 15 ) and the function ( g(x) ) shown in the table below, which has…

Explanation:

Step1: Calculate the average rate of change for (f(x))

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). For (f(x)=3x^{2}-2x + 15) and the interval ([3,7]): First, find (f(3)) and (f(7)). (f(3)=3\times(3)^{2}-2\times(3)+15=3\times9-6 + 15=27-6 + 15=36) (f(7)=3\times(7)^{2}-2\times(7)+15=3\times49-14 + 15=147-14 + 15=148) Then, the average rate of change of (f(x)) over ([3,7]) is (\frac{f(7)-f(3)}{7 - 3}=\frac{148-36}{4}=\frac{112}{4}=28)

Step2: Calculate the average rate of change for (g(x))

For the function (g(x)) and the interval ([4,9]). From the table, when (x = 4), (g(4)=82) and when (x = 9), (g(9)=257) The average rate of change of (g(x)) over ([4,9]) is (\frac{g(9)-g(4)}{9 - 4}=\frac{257-82}{5}=\frac{175}{5}=35)

Answer:

Since (28<35), (g(x)) has a greater average rate of change.