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M3-028-A05-V03
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F-IF.9
Warmup
M3-028-A05-V03
Compare functions represented algebraically, graphically, numerically, or verbally.
Compare average rates across representations
Problem
On \([0,~3]\), use graph \(f\) endpoints \((0,~5)\) and \((3,~11)\) and evaluate \(g(x)~=~3^x\). Compute \(\text{both}~\text{average}~\text{rates}\) of change, compare them, and give their difference.
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A
From 0 to 3, f rises from 5 to 11, so its average rate is 2. g rises from 1 to 27, so its average rate is 26/3; g’s rate exceeds f’s by 20/3.
B
From 0 to 3, f rises from 5 to 11, so its average rate is 1/2. g rises from 1 to 27, so its average rate is 26/3; g’s rate exceeds f’s by 20/3.
C
From 0 to 3, f rises from 5 to 11, so its average rate is 2. g rises from 1 to 27, so its average rate is 26/3; g’s rate is less than f’s by 20/3.
D
From 0 to 3, f rises from 5 to 11, so its average rate is 2. g rises from 1 to 27, so its average rate is 3/26; g’s rate exceeds f’s by 20/3.
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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
