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

For every function, we will find the average rate of change from x = -3 to x = -1

The average rate of change will be given as follows:

$\frac{f(a)-f(b)}{a-b}$

a) When F(x) = 3x

The average rate will be:

$\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3\cdot-3-(3\cdot-1)}{-3-(-1)}=\frac{-9+3}{-3+1}=\frac{-6}{-2}=3$

So, it will be positive

b) When F(x) = 3

The average rate will be:

$\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3-3}{-3+1}=\frac{0}{2}=0$

So, it will be zero

c) When f(x) = 3x^2

The average rate will be:

$\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{3\cdot9-3\cdot1}{(-3)-(-1)}=\frac{24}{-2}=-12$

So, it will be negative

d) when F(X) = 3x^2 - x

The average rate will be:

$\frac{f(-3)-f(-1)}{(-3)-(-1)}=\frac{(3\cdot9+3)-(3\cdot1+1)}{-3+1}=\frac{30-4}{-2}=\frac{26}{-2}=-13$

So, it will be negative

so, the answer will be option a) F(X) = 3x