Problem

Compare domain and range for these representations: A is the full quadratic \(y=x^{2}\); B is \(y=\sqrt{x}\).

Unworked source graphs, equation, and table containing only the supplied representations.

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What this problem is really about

Domain and range comparisons require four independent set records before any relation is named. We’ll project each representation onto its input and output axes, preserve endpoint inclusion, then compare domains with domains and ranges with ranges for equality or proper containment.

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A domain=[0,∞); A range=(-∞,∞); B domain=[0,∞); B range=[0,∞); domain relation=same; range relation=B proper subset of A; endpoint inclusion=0 included in both domains and B range

A domain=(-∞,∞); A range=[0,∞); B domain=(-∞,∞); B range=[0,∞); domain relation=same; range relation=same; endpoint inclusion=0 included in both ranges

A domain=(-∞,∞); A range=[0,∞); B domain=[0,∞); B range=[0,∞); domain relation=B proper subset of A; range relation=same; endpoint inclusion=0 included in both ranges and B domain

A domain=(-∞,∞); A range=(-∞,∞); B domain=[0,∞); B range=[0,∞); domain relation=B proper subset of A; range relation=B proper subset of A; endpoint inclusion=0 included in B domain and range

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Compare domain and range for these representations: A is the full quadratic \(y=x^{2}\); B is \(y=\sqrt{x}\).

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