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What is the amplitude of

g(x)=cos((2pi)/(3)x)+1?
units

What is the amplitude of\newlineg(x)=cos(2π3x)+1? g(x)=\cos \left(\frac{2 \pi}{3} x\right)+1 ? \newlineunits

Full solution

Q. What is the amplitude of\newlineg(x)=cos(2π3x)+1? g(x)=\cos \left(\frac{2 \pi}{3} x\right)+1 ? \newlineunits
  1. Question Prompt: The question_prompt: What is the amplitude of the function g(x)=cos(2π3x)+1g(x) = \cos\left(\frac{2\pi}{3}x\right) + 1?
  2. Identifying Amplitude: The amplitude of a trigonometric function like cosine or sine is the coefficient in front of the cosine or sine term. In the function g(x)=cos(2π3x)+1g(x) = \cos\left(\frac{2\pi}{3}x\right) + 1, the coefficient in front of the cosine term is 11.
  3. Determining Coefficient: Since there is no coefficient other than 11 in front of the cosine term, the amplitude of the function is 11. The "+1+1" outside of the cosine function shifts the graph vertically but does not affect the amplitude.
  4. Final Amplitude: Therefore, the amplitude of the function g(x)=cos(2π3x)+1g(x) = \cos\left(\frac{2\pi}{3}x\right) + 1 is 11 unit.

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