Part 2/6:
To illustrate these transformations, we will use the cosine function, specifically ( f(x) = \cos(x) ), which oscillates between -1 and 1. The fundamental properties and points of the cosine function, including its behavior at standard angles such as ( \pi/2 ) (90 degrees), ( 3\pi/2 ) (270 degrees), and ( 2\pi ) (360 degrees), provide a solid foundation for our transformations.
Vertical Stretching
Vertical stretching occurs when we multiply the function by a constant c that is greater than one.
For example, if we define a new function:
[
y_1 = 2 \cdot \cos(x)
]