Question

Function gis represented by the equation.915) = –18(3) *+ 2Which statement correctly compares the two functions on the interval [-1, 2]?

Answer 1

step 1

Find out the average rate of change function f over the interval [-1,2]

`(f(b)-f(a))/(b-a)`

we have

a=-1

b=2

f(a)=f(-1)=-22

f(b)=f(2)=-1

substitute

`(-1-(-22))/(2-(-1))=(21)/(3)=7`

step 2

Find out the average rate of change function g(x) over the interval [-1,2]

we have

a=-1

b=2

g(a)=g(-1)=-18(1/3)^-1+2=-52

g(b)=g(2)=-18(1/3)^2+2=0

substitute

`(0-(-52))/(2-(-1))=(52)/(3)=17.3`

therefore

17>7

the answer is option A