Graphing the Cosine Function with a Change in the Period

The video tutorial explains how to graph the function X equals cosine of 2X. It begins by reviewing the parent cosine graph, emphasizing the importance of understanding its amplitude and period. The tutorial then explores how the transformation affects the graph's amplitude and period, and identifies the critical points by dividing the period by four. The instructor demonstrates how to adjust the graph for the transformation and set up the axes, concluding with a complete graph of the cosine function of 2X.

What is the amplitude of the parent cosine graph?

• π

• 2

• 1

• 0.5

How does the period of the cosine function change when the function is transformed to cosine of 2X?

• It becomes 0.5π

• It remains 2π

• It changes to π

• It changes to 4π

How many critical points are there in one period of the cosine function?

• Four

• Three

• Five

• Two

What is the distance between critical points in the transformed cosine graph?

• π/4

• π/2

• 2π

• π

What is the total distance from the maximum to the minimum value of the transformed cosine graph?

• π/2

• 1

• 2

• π