Question

Which of the following functions have an average rate of change that is positive on theinterval from x = -3 to x= -1? Select all that apply.f(x) = 3xf(x) = 3f(x) = 3x2f(x) = 3x2 - x

Answer 1

The function with the positive rate of change in (-3, -1) is:

f(x) = 3x

Which function has a positive rate of change in the interval?

The average rate of change of a function f(x) in the range (a, b) is given by:

R = (f(b) - f(a))/(b - a)

Here the interval is (-3, -1)

The function with a positive rate of change in that interval is the first one, which is f(x) = 3x

f(-3) = 3*-3 = -9

f(-1) = 3*-1 = -3

The rate of change is:

R = (-3 + 9)/(-1 + 3) = 6/2 = 3