Consider the function f(x)=4sin(π2(x−3))+8. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.   Enter the exact answers.   Amplitude: A=    Period: P= Midline: y=    The phase shift is _____ . The vertical translation is_______     Hints for the maximum and minimum values of f(x): The maximum value of y=sin(x) is y=1 and the corresponding x values are x=π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=π2. The minimum value of y=sin(x) is y=−1 and the corresponding x values are  x=3π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=3π2. If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles. If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.

Question

Consider the function f(x)=4sin(π2(x−3))+8. State the amplitude A, period P, and midline. State the phase shift and vertical translation. In the full period [0, P], state the maximum and minimum y-values and their corresponding x-values.

 

Enter the exact answers.

 

Amplitude: A=   

Period: P=

Midline: y=   

The phase shift is _____

.

The vertical translation is_______

 

 

Hints for the maximum and minimum values of f(x):

  • The maximum value of y=sin(x) is y=1 and the corresponding x values are x=π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=π2.
  • The minimum value of y=sin(x) is y=−1 and the corresponding x values are  x=3π2 and multiples of 2π less than and more than this x value. You may want to solve π2(x−3)=3π2.
  • If you get a value for x that is less than 0, you could add multiples of P to get into the next cycles.
  • If you get a value for x that is more than P, you could subtract multiples of P to get into the previous cycles.

 

For x in the interval [0, P], the maximum y-value and corresponding x-value is at:

X=

Y=

For x in the interval [0, P], the minimum y-value and corresponding x-value is at:

 

X=

Y=

 

 

 

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