Transformations of the Cosine Function

The video tutorial demonstrates how to graph the function 2cos(x - π/2) + 1 by breaking down the process into steps. It starts with sketching the basic cosine function, then applies a phase shift to the right by π/2 units, adjusts the amplitude to 2, and finally shifts the graph vertically by 1 unit. The instructor explains each transformation step-by-step, ensuring a clear understanding of how each component affects the graph.

What is the primary focus of this video tutorial?

• Understanding logarithmic functions

• Solving quadratic equations

• Graphing the function 2cos(x - π/2) + 1

• Graphing linear functions

What is the value of cosine at 0 radians?

• 0

• 1

• -1

• Undefined

How does the graph of cosine change when a phase shift of π/2 is applied?

• It shifts upwards by π/2 units

• It shifts to the right by π/2 units

• It remains unchanged

• It shifts to the left by π/2 units

What effect does multiplying the cosine function by 2 have on its graph?

• It stretches the graph vertically

• It compresses the graph vertically

• It stretches the graph horizontally

• It shifts the graph to the left

What is the new range of the cosine function after adjusting the amplitude?

• [0, 2]

• [-2, 2]

• [-3, 3]

• [-1, 1]

What is the final step in graphing the function 2cos(x - π/2) + 1?

• Applying a horizontal shift

• Applying a vertical shift

• Changing the period

• Reflecting the graph

How does the vertical shift affect the graph of the function?

• It compresses the graph horizontally

• It shifts the graph down by one unit

• It shifts the graph up by one unit

• It stretches the graph vertically

What is the new y-coordinate of the point originally at (π/2, 2) after the vertical shift?

• (π/2, 0)

• (π/2, 3)

• (π/2, 2)

• (π/2, 1)

What is the y-coordinate of the point at 2π after applying the vertical shift?

• 1

• -1

• 0

• 2

What is the overall effect of the transformations on the original cosine graph?

• The graph is shifted left and compressed

• The graph remains unchanged

• The graph is stretched and shifted up

• The graph is reflected and shifted down