Question

The functions f, of, xf(x), g, of, xg(x), and h, of, xh(x) are shown below. Select the option that represents the ordering of the functions according to their average rates of change on the interval 1, is less than or equal to, x, is less than or equal to, 41≤x≤4 goes from least to greatest.
f, of, x
f(x)
x
y
xx g, of, xg(x)
11 3939
22 2828
33 1919
44 1212
55 77
h, of, x, equals, x, squared, minus, 3, x, plus, 20h(x)=x
2
−3x+20
Answer
Multiple Choice Answers
f, of, x, comma, h, of, x, comma, g, of, xf(x),h(x),g(x)
g, of, x, comma, h, of, x, comma, f, of, xg(x),h(x),f(x)
g, of, x, comma, f, of, x, comma, h, of, xg(x),f(x),h(x)
h, of, x, comma, f, of, x, comma, g, of, xh(x),f(x),g(x)
h, of, x, comma, g, of, x, comma, f, of, xh(x),g(x),f(x)
f, of, x, comma, g, of, x, comma, h, of, xf(x),g(x),h(x)
Submit Answer
Copyright ©2025 DeltaMath.com All Rights Reserved. Terms & Policies

Answer 1

g(x), f(x), h(x)

Reason: Average rates on [1,4]:
- g: (g(4)−g(1))/(4−1) = (12−39)/3 = −9
- f (f(x)=x): (4−1)/3 = 1
- h (h(x)=x^2−3x+20): (24−18)/3 = 2

So −9 < 1 < 2, i.e. g, f, h.