Problem

\(\text{Two}~\text{sinusoids}\) each have amplitude \(4\); \(f\) has midline \(y~=~2\) and \(g\) has midline \(y~=~-1\), with \(\text{no}~\text{periods}~\text{or}~\text{phases}\) supplied. Compare their deviations and ranges, then state what remains unestablished.

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Analysis: Both deviate 4 units from their centers, but their midlines and ranges differ: f has range [−2, 6] and g has range [−4, 4]. Their periods, phases, and pointwise ordering are not established.

Analysis: Both deviate 4 units from their centers, but their midlines and ranges differ: f has range [−4, 4] and g has range [−5, 3]. Their periods, phases, and pointwise ordering are not established.

Analysis: Both deviate 4 units from their centers, but their midlines and ranges differ: f has range [−2, 6] and g has range [−5, 3]. Their periods, phases, and pointwise ordering are not established.

Analysis: Both deviate 4 units from their centers, but their midlines and ranges differ: f has range [−2, 6] and g has range [−5, 3]. Their periods and phases must match because amplitudes match.

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\(\text{Two}~\text{sinusoids}\) each have amplitude \(4\); \(f\) has midline \(y~=~2\) and \(g\) has midline \(y~=~-1\), with \(\text{no}~\text{periods}~\text{or}~\text{phases}\) supplied. Compare their deviations and ranges, then state what remains unestablished.

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