Graphing the Cosine Graph with Vertical Shift

The video tutorial explains how to graph the function G(x) = 2cos(πx) + 1. It covers the standard form of the function, identifying key components like amplitude and period, and determining critical points and the X scale. The tutorial also demonstrates how to graph the function, considering vertical translations and cyclical nature of cosine graphs.

What is the role of the '+1' in the function G(x) = 2cos(πx) + 1?

• It shifts the graph horizontally.

• It changes the amplitude of the graph.

• It shifts the graph vertically.

• It alters the period of the graph.

How do you determine the amplitude of the function G(x) = 2cos(πx) + 1?

• By dividing the period by 2.

• By adding 1 to the cosine function.

• By taking the absolute value of 2.

• By taking the absolute value of π.

What is the period of the function G(x) = 2cos(πx) + 1?

• 2

• 1

• 2π

• π

How is the X scale determined for the function G(x) = 2cos(πx) + 1?

• By dividing the amplitude by 4.

• By dividing the period by 4.

• By multiplying the period by 4.

• By adding 4 to the period.

What are the start and end points of one cycle of the function G(x) = 2cos(πx) + 1?

• 0 and 1

• 0 and 2π

• 0 and π

• 0 and 2

What is the effect of a vertical translation on the graph of G(x) = 2cos(πx) + 1?

• It changes the period of the graph.

• It shifts the graph up or down.

• It alters the amplitude of the graph.

• It rotates the graph.

How does the graph of G(x) = 2cos(πx) + 1 differ from the standard cosine graph?

• It is reflected over the X-axis.

• It is shifted horizontally.

• It is shifted vertically and has a different amplitude.

• It has a different period and amplitude.