Graphing the Cosine Function with a Phase Shift

The video tutorial explains how to graph a transformed cosine function. It covers determining the amplitude, period, and critical points, and discusses the effects of transformations such as phase shifts and reflections. The tutorial provides a step-by-step guide to constructing the graph, highlighting key points and intervals, and concludes with a demonstration of graphing in both positive and negative directions.

What is the amplitude of a function if the coefficient of the cosine term is -1?

• 2

• -1

• 1

• 0

How do you calculate the period of a cosine function?

• 2π multiplied by B

• B divided by 2π

• 2π divided by B

• B multiplied by 2π

What is the distance between critical points if the period is 2π?

• π

• π/2

• 2π

• π/4

How does a negative sign in front of the cosine function affect the graph?

• It reflects the graph over the X-axis

• It stretches the graph vertically

• It shifts the graph to the left

• It shifts the graph to the right

What is the starting point of the graph after a phase shift of π/4?

• 5π/4

• π/4

• 0

• 2π

If the initial point is π/4, what is the second critical point?

• π

• 5π/4

• 3π/4

• π/2

What is the next critical point after subtracting π/2 from π/4?

• -3π/4

• π/4

• -π/4

• 3π/4