Question

How do you graph and list the amplitude, period, phase shift for `y=1/2cos(pi/4(x-2))+4`?

Answer 1

cos values `in [ - 1, 1 ]`

`y = 1/2 cos (pi/4 ( x - 2 )) + 4 in [ 4 - 1/2, 4 + 1/2 ] = [ 7/2, 9/2 ]`

Vertical shift = 4 rArr axis is `y = 4`.

Period = ( 2pi )/(pi/4) = 8

Amplitude = 1/2

Phase shift = 2

See graph,depicting all these aspects, for the simplified

`y = 1/2 sin(1/4pix) + 4`..
graph{(y-4-1/2 sin(1/4 pi x))(y-4+0x)(y-9/2+0x)(y-7/2+0x)=0[-10 10 3 6] }