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:

![http://mathworld.wolfram.com/SquareRoot.html]( useruploads.socratic.org )

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

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