Question

50 Points, Explain your answer!

Determine the function whose graph is given by (sine graph):

Determine the function whose graph is given by (cosine graph):

Answer 1

12. Answer: y = 2 sin(4x) + 1

Explanation:

The general form of a sin equation is: y = A sin (Bx - C) + D

`A=(max - min)/(2)\\\\\\.\ =(3-(-1))/(2)\\\\\\.\ =(4)/(2)\\\\\\.\ =2`

D = max - A

= 3 - 2

= 1

`\text{The period of the given graph is } (\pi)/(2)\ and\ \text{the formula for period is }(2\pi)/(B)\\\\\rightarrow (2\pi)/(B)=(\pi)/(2)\\\\\\\text{Cross multiply: }4\pi=B\pi\\\\\text{Divide both sides by }\pi: B=4`

There is no phase shift so C = 0

A = 2, B = 4, C = 0, D = 1 --> Equation of the graph is: y = 2 sin (4x) + 1

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12. Answer:
`\bold{y=(1)/(2)\ cos\bigg((1)/(2)x\bigg)}`

Explanation:

The general form of a cos equation is: y = A cos (Bx - C) + D

`A=(max - min)/(2)\\\\\\.\ =((1)/(2)-(-(1)/(2)))/(2)\\\\\\.\ =(1)/(2)`

`\text{D = max - A}\\\\.\ =(1)/(2)-(1)/(2)\\\\.\ =0`

`\text{The period of the given graph is}\ 4\pi \ and\ \text{the formula for period is }(2\pi)/(B)\\\\\rightarrow (2\pi)/(B)=4\pi\\\\\\\text{Cross multiply: }2\pi=4\pi B\\\\\text{Divide both sides by }4\pi: B=(1)/(2)`

There is no phase shift so C = 0

A =
`(1)/(2)`, B =
`(1)/(2)`, C = 0, D = 0 --> Equation of the graph is:
`y=(1)/(2)\ cos\bigg((1)/(2)x\bigg)`