What is the average rate of change of f(x)=x2+x−6 between x=3 and x=9?

13

Step-by-step explanation:

The average rate of change of a function f(x) in the closed interval [ a, b ] is

here [ a, b ] = [ 3, 9 ]

f(b) = f(9) = 9² + 9 - 6 = 84

f(a) = f(3) = 3² + 3 - 6 = 6

average rate of change = = = 13

18

step-by-step explanation:

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).