Transformations of Sinusoidal Functions

This lesson covers transformations of sinusoidal functions, focusing on shifting graphs vertically and horizontally. It explains how amplitude and period are affected by changes in parameters A and B, and how vertical and horizontal shifts are determined by k and h. Examples illustrate these concepts, showing how sine and cosine graphs can be transformed. The lesson concludes with practical applications, demonstrating that sinusoidal graphs can be modeled in multiple ways.

What happens to the amplitude of a sinusoidal function when the value of A increases?

• The amplitude remains the same.

• The amplitude becomes zero.

• The amplitude increases.

• The amplitude decreases.

How does the graph of a sinusoidal function shift when a positive value is added to k?

• It shifts to the right.

• It shifts upward.

• It shifts to the left.

• It shifts downward.

If h is positive, in which direction does the graph of a sinusoidal function move?

• To the left

• To the right

• Downward

• Upward

What is the effect of subtracting a positive value from x in a sinusoidal function?

• The graph shifts downward.

• The graph shifts upward.

• The graph shifts to the right.

• The graph shifts to the left.

Which of the following is true about the midline of a sinusoidal wave?

• It is always at y = 0.

• It changes with the value of h.

• It is unaffected by transformations.

• It is determined by the value of k.

How can a sinusoidal graph be represented using both sine and cosine functions?

• As either sine or cosine with appropriate shifts.

• It cannot be represented by both.

• Only as a cosine function.

• Only as a sine function.

What determines the starting point of the five-point pattern in sinusoidal graphs?

• The value of A

• The value of B

• The value of k

• The choice of starting on the midline or at a peak/trough