Consider the function f(x)=2sin(π2(x−3))+4

. 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=



Number





Period: P=



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Midline: y=



Number





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=



Preview Change entry mode

y=



Preview Change entry mode





For x

in the interval [0, P

], the minimum y

-value and corresponding x

-value is at:







x=



Preview Change entry mode

y=



Preview Change entry mode