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