Consider the functionf(x)=2sin(/4(x3))+4

. State the amplitudeA

, periodP

, and midline.State the phase shift and vertical translation. In the full period

[0,P

], state the maximum and minimumy

-values and their correspondingx

-values.

Enter the exact answers.

Amplitude:A=

Period:P=

Midline:y=

The phase shift is

4 units to the left

3 units to the right

4 units to the right

3 units to the left

3 units to the right

.

The vertical translation is

down 3 units

down 4 units

up 3 units

up 4 units

Click for List

.

Hints for the maximum and minimum values off(x)

:

• The maximum value ofy=sin(x)
• isy=1
• andthe correspondingx
• values arex=
• 2
• and multiples of2
• less than and more than thisx
• value. You may want to solve
• 4
• (x3)=
• 2
• .
• The minimum valueofy=sin(x)
• isy=1
• andthe correspondingx
• values arex=3
• 2
• and multiples of2
• less than and more than thisx
• value. You may want to solve
• 4
• (x3)=3
• 2
• .
• If you get a value forx
• that is less than0, you could add multiples ofP
• to get into the next cycles.
• If you get a value forx
• that is more thanP
• , you could subtract multiples ofP
• to get into the previous cycles.

Forx

in the interval [0,P

], themaximumy

-value and correspondingx

-value is at:

x=

y=

Forx

in the interval [0,P

], theminimumy

-value and correspondingx

-value is at:

x=

y=