Final Answer:
The transformation of y=cosx that shifts it 3 units to the right and has a frequency of 2x is = cos(2−3)y=cos(2x−3).
Step-by-step explanation:
The transformation involves two key modifications to the original cosine function. Firstly, there is a horizontal shift to the right, which is represented by the term inside the cosine function cos(2−3)cos(2x−3).
The subtraction of 3 units inside the parentheses indicates the rightward shift of the graph by 3 units.
Secondly, there is a change in frequency, represented by the 2x inside the cosine function. The coefficient of 2 before x increases the frequency of the cosine wave, meaning it completes two cycles for every unit increase in x. This results in a compression of the graph horizontally.
In summary, the transformed function =cos(2−3)y=cos(2x−3) incorporates both a rightward shift of 3 units and a frequency change of 2x compared to the original =cos y=cosx function.