Master Graphing Cosine with a change in the Amplitude

The video tutorial explains how to graph cosine functions with changes in amplitude. It begins with an introduction to cosine graphs and the concept of the initial period. The tutorial then delves into understanding amplitude, explaining how it affects the graph's maximum and minimum points. The instructor demonstrates graphing a cosine function with an amplitude of 2, showing how the graph stretches vertically. Finally, the tutorial covers graphing with an amplitude of -1/2, highlighting the reflection over the X-axis and vertical compression.

What is the initial period of a cosine graph?

• The time it takes for the graph to complete one full cycle.

• The distance between the maximum and minimum points.

• The starting point of the graph on the Y-axis.

• The amplitude of the graph.

How is the amplitude of a cosine graph defined?

• The half distance between the maximum and minimum points.

• The total height of the graph.

• The distance from the X-axis to the maximum point.

• The distance from the origin to the first peak.

What happens to the cosine graph when the amplitude is increased to 2?

• The graph shifts to the right.

• The graph stretches vertically.

• The graph compresses horizontally.

• The graph remains unchanged.

When graphing two full periods of a cosine function, what remains unchanged?

• The phase shift.

• The amplitude.

• The Y-intercept.

• The X scale and period.

How does a negative amplitude affect the cosine graph?

• It shifts the graph upwards.

• It reflects the graph over the X-axis.

• It compresses the graph horizontally.

• It stretches the graph vertically.

What is the effect of an amplitude less than one on the cosine graph?

• The graph is horizontally compressed.

• The graph is vertically compressed.

• The graph is vertically stretched.

• The graph is horizontally stretched.

What is the absolute value of the amplitude when it is -1/2?

• 0

• 1

• -1/2

• 1/2