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M2-025-A09-V02
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F-IF.9
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M2-025-A09-V02
Compare function properties across representations, especially quadratic comparisons.
Compare two domain and range set records
Problem
Compare domain and range for these representations: A is a projectile model with \(0\le~t\le~4\) and \(0\le~h\le~64\); B is unrestricted \(h=-16(t-2)^{2}+64\).
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A
A domain=(-∞,∞); A range=[0,64]; B domain=(-∞,∞); B range=(-∞,64]; domain relation=same; range relation=A proper subset of B; endpoint inclusion=0 and64 included in A range
B
A domain=(-∞,∞); A range=(-∞,64]; B domain=[0,4]; B range=[0,64]; domain relation=B proper subset of A; range relation=B proper subset of A; endpoint inclusion=0,4,and64 included for B
C
A domain=[0,4]; A range=[0,64]; B domain=[0,4]; B range=[0,64]; domain relation=same; range relation=same; endpoint inclusion=all finite endpoints included
D
A domain=[0,4]; A range=[0,64]; B domain=(-∞,∞); B range=(-∞,64]; domain relation=A proper subset of B; range relation=A proper subset of B; endpoint inclusion=all finite endpoints included
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Curriculum context
Standard F-IF.9
Category Functions
Domain Interpreting Functions
Objective Compare function properties across representations, especially quadratic comparisons.
Problem type Compare two domain and range set records