Sinusoidal Function Transformations
Every sinusoid is a·sin(b(x−h))+k: amplitude |a| (reflection when a is negative), period 2π/|b|, phase shift h, midline k. The two laws that carry the topic: b is a compression factor, not the period, and the shift is only readable after factoring b out of the argument: sin(2x+π) shifts left π/2, not π. Inside signs read backward: (x−h) moves right.
The mistakes are role mistakes: b quoted as the period, the unfactored constant quoted as the shift, shifts run the wrong direction, and maxima or vertical shifts quoted as amplitude. The lesson drills each dial separately, then together.
The work
3 ways in · any order
Lesson
Sinusoidal Function Transformations
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Four dials, read in order: amplitude and midline, then the 2π/|b| period law, then the factor-first phase read. The lesson closes with ten scenarios where every dial has a tempting wrong reading, including the unfactored arguments that hide their shifts.
Diagnostic
10-item topic check
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Ten items spanning the three Topic 3.6 misconceptions: b-as-period errors, amplitude and midline misreads, and phase shifts read without factoring or run the wrong direction. Results route you to the drills that fix what fired.
Targeted Practice
Drill a single misconception
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Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.