Write an equation for the translation of the function. y = cos x; translated 6 units up.

Solution:

If the function y = cos x is translated 6 units can have two implications:

1. The transformed function becomes y = 6cosx or
2. The transformed function becomes y = cos6x

Stretching is observed in both cases. Both transformations have been depicted in the graph below:

1. Graph of 6 cos x has stretched vertically with the increase in the amplitude of y = cos x.
2. While the function cos 6x has stretched vertically as compared to the graph of cos x but its vertical stretch is quite small when compared to y = 6cosx

Write an equation for the translation of the function. y = cos x; translated 6 units up.

Summary:

The equation(s) for the translation of the function. y = cos x; translated 6 units up is 6cos(x).