Understanding Sinusoidal Functions

The video tutorial explains how to derive a sinusoidal function from a given graph. It covers identifying key points, calculating the midline, amplitude, period, and horizontal shift. The tutorial also explores alternative function representations and demonstrates how different equations can represent the same graph.

What are the coordinates of the points through which the sinusoidal function passes?

• (-2, -5) and (4, -5)

• (-3, -6) and (1, -6)

• (-4, -7) and (2, -7)

• (-5, -8) and (3, -8)

What is the midline of the sinusoidal function?

• y = -2

• y = -3

• y = -4

• y = -5

What is the amplitude of the sinusoidal function?

• 2

• 3

• 5

• 4

What is the value of 'a' in the sinusoidal function?

• 3

• -3

• -4

• 4

What is the period of the sinusoidal function?

• 7

• 5

• 4

• 6

What is the value of 'b' in the sinusoidal function?

• 1/5π

• 1/3π

• 1/2π

• 1/4π

What is the horizontal shift 'd' for the first possible equation?

• -3

• -4

• -1

• -2

What is the horizontal shift 'd' for the second possible equation?

• -1

• -4

• -2

• -3

What remains unchanged when considering alternative equations for the sinusoidal function?

• Horizontal Shift

• Period

• Amplitude

• Vertical Shift

What is the vertical shift 'c' in the sinusoidal function?

• -1

• -2

• -3

• -4