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M3-028-A05-V02
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F-IF.9
Warmup
M3-028-A05-V02
Compare functions represented algebraically, graphically, numerically, or verbally.
Compare average rates across representations
Problem
On \([1,~4]\), compute the endpoint values and average rates of change of \(f(x)~=~\sqrt{x}\) and table \(g\) with \(g(1)~=~1\) and \(g(4)~=~7\). Compare the rates and give their difference.
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A
From 1 to 4, f rises from 1 to 2, so its average rate is 1/3. g rises from 1 to 7, so its average rate is 2; g’s rate exceeds f’s by 5/3.
B
From 1 to 4, f rises from 1 to 2, so its average rate is 1/3. g rises from 1 to 7, so its average rate is 1/2; g’s rate exceeds f’s by 5/3.
C
From 1 to 4, f rises from 1 to 2, so its average rate is 1/3. g rises from 1 to 7, so its average rate is 2; g’s rate is less than f’s by 5/3.
D
From 1 to 4, f rises from 1 to 2, so its average rate is 3. g rises from 1 to 7, so its average rate is 2; g’s rate exceeds f’s by 5/3.
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Curriculum context
Standard F-IF.9
Category Functions
Domain Interpreting Functions
Objective Compare functions represented algebraically, graphically, numerically, or verbally.
Problem type Compare average rates across representations
