:choose the function whose graph is given by:

The function of the graph is y = 3 cos (4x) ⇒ answer A

Step-by-step explanation:

- If the equation is y = A cos (B x)  

* A is the amplitude  

- The amplitude is the height from highest to lowest points and  

  divide the answer by 2  

* The period is 2π/B  

- The period is the distance from one peak to the next peak

* Lets look to the graph

- The maximum value is 3 and the minimum value is -3

∵ The height from the maximum point to the minimum point is

   3 - (-3) = 3 + 3 = 6

∴ The amplitude is 6/2 = 3

∵ A is the amplitude

∴ A = 3

- The distance between two consecutive peaks is π/2

∵ The period is the distance from one peak to the next peak

∴ The period = π/2

∵ The period = 2π/B

∴ 2π/B = π/2 ⇒ divide both sides by π

∴ 2/B = 1/2 ⇒ by using cross multiplication

∴ B = 4

- Lets write the form of the function

∵ y = A cos (Bx)

∵ A = 3 and B = 4

∴ y = 3 cos (4x)

* The function of the graph is y = 3 cos (4x)

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step-by-step explanation: