Question

How do you graph and list the amplitude, period, phase shift for `y=1/2cosx+5/2`?

Answer 1

Amplitude `1/2`, period`=2pi` and phase shift`=0` (none).

Explanation:

The general equation of cosine is `y=Acos(Bx-C)+D` where

`A=` amplitude
`(2pi)/absB=` period
`C/B=` phase shift
`D=` vertical shift

For the equation `y=1/2cosx+5/2`
`A=1/2`, `B=1`, `C=0`, `D=5/2`
Amplitude = `1/2`
Period=`(2pi)/abs1=2pi` (the "regular" period of cosine)
Phase shift = `0/1 =0` (no phase shift)
Vertical shift =`5/2` (up `5/2`)