Consider the function f(x)= 3sin(π/3(x−4))+5. 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...

Consider the function f(x)= 3sin(π/3(x−4))+5. 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:

a. up 4 units

b. 4 units to the right

c. 4 units to the left

d. 5 units to the left

The vertical translation is:

a. up 4 units

b. down 5 units

c. up 5 units

d. down 4 units

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=π/2 and multiples of 2π less than and more than this x value. You may want to solve π/3(x−4)=π/2.


• The minimum value of y=sin(x) is y=−1 and the corresponding x values are  x=3π/2 and multiples of 2π less than and more than this x value. You may want to solve π/3(x−4)=3π/2.


• 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:

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