Problem

Normalize \(y~=~-5\sin((\pi~/6)x)~-~3\). State \(A\), \(B\), \(h\), and \(D\); give the amplitude and reflection, period and quarter-period, phase shift, midline, and range.

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Normalized form: y=−5sin((π/6)(x−0))−3. Parameters: A=−5, B=π/6, h=0, D=−3; amplitude 5; reflected. Period 12; quarter-period 3; no shift; midline y=−3; range [−8,2].

Normalized form: y=−5sin((π/6)(x−0))−3. Parameters: A=−5, B=π/6, h=0, D=−3; amplitude −5; no reflection. Period 12; quarter-period 3; no shift; midline y=−3; range [−8,2].

Normalized form: y=−5sin((π/6)(x−0))−3. Parameters: A=−5, B=π/6, h=0, D=−3; amplitude 5; reflected. Period π²/3; quarter-period π²/12; no shift; midline y=−3; range [−8,2].

Normalized form: y=5sin((π/6)(x−0))−3. Parameters: A=5, B=π/6, h=0, D=−3; amplitude 5; no reflection. Period 12; quarter-period 3; no shift; midline y=−3; range [−8,2].

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Normalize \(y~=~-5\sin((\pi~/6)x)~-~3\). State \(A\), \(B\), \(h\), and \(D\); give the amplitude and reflection, period and quarter-period, phase shift, midline, and range.

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