What cosine function represents a amplitude of 3, a period of #pi#, no horizontal shift, and a vertical shift of 2?

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JDOaties3590 JDOaties3590

21-05-2018
Mathematics

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What cosine function represents a amplitude of 3, a period of #pi#, no horizontal shift, and a vertical shift of 2?

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11beehshahbaz 11beehshahbaz · Answer 1 · 2018-06-01T04:10:25+02:00

The parent cosine function is:

[tex]y=cos(x)[/tex]

The amplitude of the given function is 3, so the equation becomes:

[tex]y=3cos(x)[/tex]

The period of parent cosine function is 2π. In order to have a period of π, x will be multiplied by 2. So the function becomes:

[tex]y=3cos(2x)[/tex]

There is no horizontal shift. There is a vertical shift of 2, so 2 will be added to the function value. Thus the final expression for the function becomes:

[tex]y=3cos(2x)+2[/tex]