How do you find the domain & range for #y=7cos[3pi(x-2)]+7#?

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Answer 1 · 2018-08-02T10:10:14

Domain: #x in ( - oo, oo )#
Range: #[ - 7, 7 ]#

Any cosine value #in [ - 1 , 1 ]#. So,

#y = 7 cos ( 3 pi ( x - 2 ) + 7 = 7 cos (3 pi x - 6 pi ) + 7#

#= 7 cos (3 pi x ) + 7 in 7 [ - 1, 1 ] = [ -7, 7 ]#

Amplitude of this cosine wave: 7

Period : #( 2 pi )/(3pi)=2/3#

Vertical shift: 7

See graph.
graph{(y-7 cos(3pix)-7)(y-7+0x)(y-14+0x)(y+0x)(x-1/3+0.0001y)(x+1/3+0.0001y)=0[-0.7 0.7 -0.6 14.1 ]}

Observe the axis shift by 7 units. The graph is not on uniform scale.