Identify the amplitude and the period of the function c(x) = 3cos (x + π).

amplitude = 3

period = 2π/1 = 2π

Thank you, Steve! :)

To identify the amplitude and period of the function c(x) = 3cos(x + π), we need to understand the general form of a cosine function and how it affects the graph.

The general form of a cosine function is given by:
f(x) = A * cos(Bx + C)

In this case, we have c(x) = 3cos(x + π), where A = 3, B = 1, and C = π.

1. Amplitude (A):
The amplitude (A) represents the maximum value that the cosine function reaches vertically. In this case, A = 3, so the maximum value of c(x) is 3. The amplitude is always positive since the cosine function oscillates between -1 and 1.

2. Period (T):
The period (T) represents the length of one complete cycle of the cosine function. To determine the period, we need to compute the value of 2π/B.

In this case, B = 1, so the period (T) is given by:
T = 2π/1 = 2π.

Therefore, the amplitude of the function c(x) = 3cos(x + π) is 3, and the period is 2π.