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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 3, is less than or equal to, x, is less than or equal to, 53≤x≤5 goes from least to greatest.
f, of, x
f(x)
x
y
xx g, of, xg(x)
minus, 1−1 1919
11 99
33 77
55 1313
77 2727
h, of, x, equals, x, squared, plus, 2, x, plus, 20h(x)=x
2
+2x+20
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Multiple Choice Answers
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)
g, of, x, comma, h, of, x, comma, f, of, xg(x),h(x),f(x)
f, of, x, comma, h, of, x, comma, g, of, xf(x),h(x),g(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)
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Answer 1

I can’t read the f and g data clearly from the text you pasted. To rank the average rates of change on [3,5] I need f(3), f(5), g(3), and g(5). (The average rate of change of a function p on [3,5] is (p(5) − p(3))/(5 − 3) = (p(5) − p(3))/2.)

I can compute h’s average rate of change now:
- h(x) = x^2 + 2x + 20 ⇒ h(3) = 35, h(5) = 55
- average rate for h on [3,5] = (55 − 35)/2 = 10

Please either
- paste the values f(3), f(5), g(3), g(5), or
- attach/describe the f and g graphs or tables clearly,

and I’ll compute the two remaining average rates and give the ordering from least to greatest.