Graphing y = 3sin(2x - π/2) + 1

Trigonometry · Axiom Academy

EXAMPLE Graphing Transformed Sine Functions Learn to identify amplitude, period, phase shift, and vertical shift step-by-step to sketch trigonometric functions. Excellent work! You've successfully identified all transformations for a sine function. Here's what we learned: Standard Form: For y = A sin(Bx - C) + D, each parameter controls a specific transformation Amplitude |A|: Determines the vertical stretch/compression and distance from midline to max/min Period = 2π/B: Determines the horizontal length of one complete cycle Phase Shift = C/B: Requires factoring B from the parentheses first! Factor to get B(x - C/B) Vertical Shift = D: Moves the entire graph up or down, shifting the midline Order Matters: Apply horizontal transformations (period, phase shift) before vertical transformations (amplitude, vertical shift) Graphing Strategy: Identify midline, find starting point, mark one complete period, plot max/min points This systematic approach works for all trigonometric functions! Practice identifying transformations before graphing to build confidence and accuracy.

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