Consolidation 1

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Consolidation 1. For the function f(1) = SinI, sketch the graph of the original and transformed function and state the key features of the transformed function. a) y=f(I —30) —1 b) y = -2f(-r) + 4 c) y = —2f(—(.r + 60)) — 3 d) y = 351771 (int — 90)) 2. The graph of f(1) = sin is transformed by a vertical reflection, then a horizontal compression by a factor of 2, then a phase shift 30 degrees to the right, and finally a vertical translation of 5 units up. a) What is the equation of the transformed function? b) What are the key features of the transformed function? 3. Describe the transformations from f(1) = sinI (the red graph) that could generate 9(1) (the blue graph) below. 1 0:5 ~0:5

9 Communication 1. Write a brief summary of: a) Horizontal and vertical translations of sinusoidal functions. b) Horizontal and vertical stretches and compressions of sinusoidal functions. 0) Horizontal and vertical reflections of sinusoidal functions. 2. Which transformations change the shape of a sinusoidal function? Describe the manner in which they change the shape. 3. Which transformations change the location of a sinusoidal function? Describe the manner in which they change the location. 4. Describe the transformations to the graph of f(.r) = 6051 to produce each of the following functions. a) g(.r) = 2 f(.r — 60) + 1 b) gm = 3f(—%I) C) 9(1) = écos?r + 45) + 2 d) g(.r) = 4cos(2.t — 90) — 3 an n .. A . -. ‘1. III, . n I n