How do you graph #y=sqrt(x-1)-3#?

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Answer 1 · 2015-06-06T13:10:34

Be #Y = y+3# and #X=x-1#

The function #Y=sqrtX# has a domain going from
#X=0# to #X=+oo#
and a range going from
#Y_0 = sqrt0 = 0# to #Y_(+oo) = sqrt(+oo) = +oo#.

Its curve is as represented bellow:

However, #Y=y+3 harr y=Y-3#
therefore the #y=f(X)# curve will be identical to the #Y=f(X)# curve, only with a negative vertical offset of 3.

enter image source here

Now #X=x-1 harr x=X+1#
therefore the #y=f(x)# curve will be identical to the #y=f(X)# curve, only with a positive horizontal offset of 1.

enter image source here