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Which is the transformation of y = cos x that shifts it 3 right and has a frequency of 2x

User Void
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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.

User Aroooo
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