Question

Choose the function whose graph is given by:O A. y= cos(4x)O B. y = cos(2x)O C. y= cos(4x)O D. y= cos(4x)

Answer 1

Let's put more details in the given graph:

For us to be able to determine the equation of the given graph, we will be applying the following formula:

`\text{ y = A }\cdot\text{ Cos \lparen Bx + C\rparen + D}`

Where,

A = Amplitude

B = 2π/Period

C = Phase Shift

D = Vertical Shift

Let's determine their values.

A = Amplitude

`\text{ Amplitude = }\frac{\text{ y}_(Max)\text{ - y}_(Min)}{2}\text{ = }\frac{1\text{ - \lparen-1\rparen}}{2}\text{ = }\frac{1\text{ + 1}}{2}\text{ = }(2)/(2)\text{ = 1}`

Therefore, the Amplitude is 1.

B = 2π/Period

`\text{ Period = }(2π)/(B)`
`\text{ \pi = }(2π)/(B)`
`\text{ B = }(2π)/(π)`
`\text{ B = 2}`

Therefore, B = 2

C = Phase Shift

`\text{ C = Phase Shift = 0}`

D = Vertical Shift

`\text{ D = Vertical Shift = 0}`

In Summary, we have A = 1, B = 2, C = 0 and D = 0.

Let's now plug it to the formula to get the equation of the graph.

`\text{ y = A }\cdot\text{ Cos\lparen Bx + C\rparen + D}`
`\text{ y = \lparen1\rparen }\cdot\text{ Cos\lparen\lparen2\rparen x + 0\rparen + 0}`
`\text{ y = Cos\lparen2x\rparen}`

Therefore, the equation of the graph is y = Cos(2x).

The answer is CHOICE B : y = cos(2x)