Question

Given the function h(x) = 4x, Section A is from x = 0 to x = 1 and Section B is from x = 2 to x = 3.

Answer 1

Answer with explanation:

The average rate of change in a function f(x) from x=a to x=b is given by :-

$k=\dfrac{f(b)-f(a)}{b-a}$

For Section A .

The average rate of change in a function h(x)=4x from x=0 to x=1 is given by :-

$k=\dfrac{h(1)-h(0)}{1-0}\\\\=\dfrac{4-0}{1}=4$

For section B .

The average rate of change in a function h(x)=4x from x=2 to x=3 is given by :-

$k=\dfrac{h(3)-h(2)}{3-2}\\\\=\dfrac{12-8}{1}=4$

The average rate of section A is same for section B because the function is a linear function, and the rate of change of a linear function is constant.