Phase Shift and Cosine Functions

The video tutorial explains how to transform and graph a cosine function by identifying key parameters such as C, A, B, and D. It covers vertical and horizontal translations, amplitude, and period calculations. The tutorial guides viewers through graphing one period of the cosine function and completing the graph with key points and patterns.

What is the value of C in the given cosine function?

• -2

• 2

• -1

• 1

How does a negative value of C affect the graph of the cosine function?

• Shifts the graph up

• Reflects the graph over the y-axis

• Shifts the graph down

• Reflects the graph over the x-axis

What is the amplitude of the cosine function if A is 4?

• 2

• 4

• 8

• 6

How is the period of the cosine function calculated?

• 2π divided by A

• 2π divided by B

• π divided by B

• π divided by A

What is the period of the function if B is 2?

• π/2

• π

• 3π

• 2π

What is the phase shift if D is -1/6π?

• Right π units

• Left 1/6π units

• Right 1/6π units

• Left π units

What is the maximum value of the function if the midline is y = -1 and the amplitude is 4?

• 3

• -3

• 5

• -5

What is the pattern of the basic cosine function over one period?

• Midline, minimum, midline, maximum

• Midline, maximum, midline, minimum

• Maximum, midline, minimum, midline

• Minimum, midline, maximum, midline

What is the new position of the point (0, 1) after the phase shift?

• (1/6π, -3)

• (1/6π, 3)

• (-1/6π, 3)

• (-1/6π, -3)

What is the point that is half of the period to the right of the phase shift?

• (π/3, 5)

• (π/3, -5)

• (1/3π, -5)

• (1/3π, 5)