Sinusoidal Function Transformations and Phase Shifts

This video tutorial covers sinusoidal function transformations, focusing on the roles of parameters A, B, C, and D. It explains how to determine amplitude, midline, period, and phase shifts, and demonstrates graphing techniques for sinusoidal functions. The tutorial includes problem-solving examples and guides viewers in creating sinusoidal equations from given attributes. The session concludes with a practical application of these concepts in graph analysis.

What does the constant A affect in a sinusoidal function?

• The phase shift of the function

• The amplitude of the function

• The vertical shift of the function

• The period of the function

How does the constant B affect a sinusoidal function?

• It changes the vertical shift

• It changes the frequency

• It changes the phase shift

• It changes the amplitude

What is the effect of a positive constant C inside the parentheses of a sinusoidal function?

• It decreases the amplitude

• It shifts the function to the right

• It increases the amplitude

• It shifts the function to the left

If the period of a sinusoidal function is 2π, what is the frequency?

• 1/π

• π

• 1/2π

• 2π

How do you determine the maximum value of a sinusoidal function?

• By multiplying the amplitude by the period

• By dividing the amplitude by the period

• By subtracting the amplitude from the midline

• By adding the amplitude to the midline

What is the phase shift of the function y = -2 sin(2(x - π/2))?

• π to the right

• π/2 to the right

• π to the left

• π/2 to the left

In a sine function with a negative amplitude, which direction does the graph move first?

• Down

• Up

• Left

• Right

What is the period of the function y = -2 sin(2(x - π/2))?

• π

• π/2

• 4π

• 2π

How do you find the value of B if the period of a sinusoidal function is given?

• B = 1 / period

• B = period * 2π

• B = period / 2π

• B = 2π / period

If a sine function has a vertical shift down by 4 units, what is the value of D?

• 4

• 2

• -4

• -2