Transformations of Trigonometric Functions

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, changes the amplitude, and finally adds a vertical shift. The instructor explains each transformation and its effect on the graph, providing a clear understanding of how to graph trigonometric functions with transformations.

What is the function being graphed in this video?

• 2cos(x - π/2) + 1

• 2sin(x - π/2) + 1

• cos(x - π/2) + 2

• 2cos(x + π/2) + 1

What is the value of cosine at 0 radians?

• 1

• Undefined

• 0

• -1

How does the phase shift affect the graph of cosine?

• It shifts the graph down by π/2 units.

• It shifts the graph up by π/2 units.

• It shifts the graph to the right by π/2 units.

• It shifts the graph to the left by π/2 units.

What is the new amplitude of the function after transformation?

• 0

• -2

• 2

• 1

What is the effect of the vertical shift on the graph?

• It shifts the graph to the left by one unit.

• It shifts the graph up by one unit.

• It shifts the graph to the right by one unit.

• It shifts the graph down by one unit.

After applying all transformations, what is the y-coordinate of the point originally at (0, 1)?

• 1

• 3

• 2

• 0

What is the y-coordinate of the point at π/2 after all transformations?

• 2

• 1

• 3

• 0

What is the y-coordinate of the point at π after all transformations?

• 0

• 2

• 3

• 1

What is the y-coordinate of the point at 3π/2 after all transformations?

• -2

• -1

• 1

• 0

What is the final y-coordinate of the point at 2π after all transformations?

• 0

• 3

• 1

• 2