Transformations of the Cosine Function

The video tutorial explains how to graph the function y = -2.5 cos(1/3 x) over the interval 0 to 6π. It begins by graphing the basic cosine function, then modifies it to cos(1/3 x), stretching the period. Finally, it applies a transformation to -2.5 cos(1/3 x), adjusting the amplitude and reflecting the graph over the x-axis.

What is the initial function that the teacher plans to graph?

• y = cos(x)

• y = -2.5 cos(1/3 x)

• y = 2.5 sin(x)

• y = sin(x)

What is the period of the function y = cos(x)?

• 3π

• 2π

• π

• 6π

How does multiplying x by 1/3 affect the graph of y = cos(x)?

• It stretches the graph horizontally.

• It compresses the graph horizontally.

• It reflects the graph over the x-axis.

• It shifts the graph vertically.

What is the new period of the function y = cos(1/3 x)?

• 9π

• 6π

• 2π

• 3π

What is the effect of multiplying the cosine function by -2.5?

• It shifts the graph to the right.

• It shifts the graph upwards.

• It stretches the graph vertically and reflects it over the x-axis.

• It compresses the graph vertically.

What is the amplitude of the function y = -2.5 cos(1/3 x)?

• 2.5

• 3

• 1

• 5

How does the negative sign in -2.5 affect the graph of the cosine function?

• It shifts the graph upwards.

• It reflects the graph over the y-axis.

• It reflects the graph over the x-axis.

• It compresses the graph horizontally.

What is the difference between the maximum and minimum values of y = -2.5 cos(1/3 x)?

• 2

• 7.5

• 2.5

• 5

What is the final transformation applied to the graph of y = cos(1/3 x) to obtain y = -2.5 cos(1/3 x)?

• Horizontal compression

• Horizontal stretch

• Vertical shift

• Vertical stretch and reflection

What is the overall effect of the transformations on the graph of y = cos(x) to obtain y = -2.5 cos(1/3 x)?

• Vertical compression and horizontal reflection

• Horizontal compression and vertical shift

• Horizontal stretch and vertical reflection

• Vertical stretch and horizontal shift