Consider the functionf(x)=3sin(/4(x5))+5 . 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.

Amplitude:A=

Period:P=

Midline:y=

The phase shift is...

.The vertical translation is...

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(x5)=/2

-The minimum valueofy= sin(x)isy= 1 andthe correspondingx values arex=3/2and multiples of2less than and more than thisx value. You may want to solve/4(x5)=3/2. If you get a value forxthat is less than0, you could add multiples ofPto 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=