Graph Phase Shift State the amplitude period and

Graph Phase Shift State the amplitude, period, and phase shift for the function y = 2 sin (θ + 20°). Then graph the function. Since a = 2 and b = 1, the amplitude and period of the function are the same as y = 2 cos . However h = – 20 , so the phase shift is – 20. Because h < 0, the parent graph is shifted to the left. To graph y = 2 sin ( + 20 ), consider the graph of y = 2 sin . Graph this function and then shift the graph 20 to the left.

Graph Phase Shift Answer: amplitude: 2; period: 360°; phase shift: 20° left

Graph Vertical Translations State the amplitude, vertical shift, and equation of the midline, for. Then graph the function. amplitude: period: vertical shift: k = 3, so the midline is the graph of y = 3.

Graph Vertical Translations Since the amplitude of the function is lines parallel to the midline that are below the midline. Then draw the cosine curve. Answer: vertical shift: +3; midline: y = 3; amplitude: period: 2π , draw dashed unit above and

Graph Transformations State the amplitude, period, phase shift, and vertical shift for Then graph the function. The function is written in the form y = a cos [b(θ – h) + k]. Identify the values of a, b, and k. a = 3, so the amplitude is |3| or 3. b = 2, so the period is h= or π. so the phase shift is right. k = 4, so the vertical shift is 4 units up.

Graph Transformations Graph the function. Step 1 The vertical shift is 4. Graph the midline y = 4.

Graph Transformations Step 2 The amplitude is 3. Draw dashed lines 3 units above and below the midline at y = 1 and y = 7.

Graph Transformations Step 3 The period is π, so the graph is compressed. Graph y = 3 sin 2θ + 4 using the midline as a reference.

Graph Transformations Step 4 Answer: Shift the graph to the right.