How to Graph the Sine Function by Applying a Phase Shift and Vertical Translation

The video tutorial demonstrates how to graph the function F(x) = sin(x + π/6) + 1. It covers understanding transformations, calculating parameters like amplitude, period, phase shift, and vertical shift, and graphing each translation step by step. The tutorial also explains determining the X scale and finalizing the graph with amplitude and vertical shift adjustments.

What is the function F(x) that is being graphed in the video?

• F(x) = sin(x - π/6) + 1

• F(x) = cos(x + π/6) + 1

• F(x) = sin(x + π/6) + 1

• F(x) = tan(x + π/6) + 1

Which transformation is responsible for shifting the graph vertically?

• Vertical Translation

• Phase Shift

• Period

• Amplitude

How is the phase shift calculated for the function F(x) = sin(x + π/6) + 1?

• Set x + π/6 = 0

• Set x - π/3 = 0

• Set x - π/6 = 0

• Set x + π/3 = 0

What is the period of the function F(x) = sin(x + π/6) + 1?

• π

• π/3

• 2π

• π/2

What is the distance between each X scale point in the graph?

• π/3

• π/4

• π/2

• π/6

How many complete periods are graphed in the video?

• One

• Two

• Three

• Four

What is the maximum value reached by the graph after vertical translation?

• 3

• 2

• 1

• 0