Graphing the Cosine Curve with a Period Shift

The video tutorial explains how to analyze and graph the function F(x) = 2cos(x + π). It covers finding the amplitude and period, determining critical points, and graphing the function with transformations. The tutorial also compares the transformed graph with the parent cosine function, highlighting changes in amplitude and starting points.

What is the amplitude of the function F(x) = 2cos(x + π)?

• 1

• 0

• 2

• π

How do you calculate the period of the function F(x) = 2cos(x + π)?

• 2π / 2

• π / 2

• π

• 2π / 1

What is the distance between critical points for the function F(x) = 2cos(x + π)?

• 2π

• π/4

• π

• π/2

What are the start and end points of one period of the function F(x) = 2cos(x + π)?

• 0 to 2π

• -π to π

• -2π to 0

• π to 2π

How does the amplitude affect the graph of the function F(x) = 2cos(x + π)?

• It stretches the graph vertically

• It reflects the graph over the x-axis

• It shifts the graph horizontally

• It compresses the graph horizontally

What is the significance of the critical points in graphing the function F(x) = 2cos(x + π)?

• They determine the amplitude

• They help in plotting maximum, minimum, and intercepts

• They indicate the start and end of the graph

• They define the period

Why is it important to understand transformations when graphing trigonometric functions?

• To determine the amplitude

• To accurately plot the graph

• To find the period

• To solve equations