Question

Consider functions f, g, and h below.

Order the above functions, from least to greatest, by the rate of change of functions over the interval [0, 2].

g, h, f

f, h, g

f, g, h

g, f, h

Answer 1

We evaluate f (x) between [0, 2]
We have then:
f (x) = x2 + 2x +3
f (0) = (0) 2 + 2 (0) +3 = 3
f (1) = (1) 2 + 2 (1) +3 = 6
f (2) = (2) 2 + 2 (2) +3 = 11
We observe that the function g between [0, 2] is between 4 and 7
We observe that the function h is a linear equation whose rate of change is constant and equal to three.
Answer:
from least to greatest, by the rate of change of functions over the interval [0, 2] we have:
g, h, f