Understanding Sine Function Transformations

The video tutorial explains how to determine the equation of a graph using the sine function. It begins with a review of the basic sine function components, such as period, midline, maximum, and minimum. The tutorial then focuses on analyzing a specific graph, highlighting one period to determine the transformation. It calculates the values of B and C, discusses amplitude and reflection, and concludes by writing the equation of the graph. The tutorial emphasizes that different graph sections can lead to different equations but represent the same graph.

What is the range of one period of the basic sine function?

• 0 to π/2

• 0 to 4π

• 0 to π

• 0 to 2π

If a graph completes one cycle from 0 to 6, what is the period of the function?

• 2π units

• 6 units

• 3 units

• 12 units

What is the value of B if the period of the sine function is 6?

• π/3

• 2π

• π/6

• 3π

What is the midline of a graph if it is shifted down by one unit?

• y = -2

• y = -1

• y = 1

• y = 0

What is the vertical shift if the midline is at y = -1?

• Shifted up 1 unit

• Shifted down 1 unit

• No shift

• Shifted up 2 units

How is the amplitude of a sine function determined?

• Distance from minimum to x-axis

• Distance from midline to maximum

• Distance from maximum to minimum

• Distance from midline to x-axis

What does a negative amplitude indicate about the graph?

• It is stretched vertically

• It is shifted up

• It is reflected across the midline

• It is shifted down

What is the amplitude of a sine function if the distance from the midline to the maximum is 3 units?

• 2 units

• 1 unit

• 4 units

• 3 units

If a sine function starts at the midline and goes down first, what does this indicate?

• A vertical shift

• A phase shift

• An increase in amplitude

• A reflection across the midline

What is the equation of the sine function if A = -3, B = π/3, and C = -1?

• y = -3 sin(π/3 x) + 1

• y = -3 sin(π/3 x) - 1

• y = 3 sin(π/3 x) - 1

• y = 3 sin(π/3 x) + 1