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

Jun 6, 2015

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

The function $Y = \sqrt{X}$ has a domain going from
$X = 0$ to $X = + \infty$
and a range going from
${Y}_{0} = \sqrt{0} = 0$ to ${Y}_{+ \infty} = \sqrt{+ \infty} = + \infty$.

Its curve is as represented bellow:

However, $Y = y + 3 \leftrightarrow y = Y - 3$
therefore the $y = f \left(X\right)$ curve will be identical to the $Y = f \left(X\right)$ curve, only with a negative vertical offset of 3.

Now $X = x - 1 \leftrightarrow x = X + 1$
therefore the $y = f \left(x\right)$ curve will be identical to the $y = f \left(X\right)$ curve, only with a positive horizontal offset of 1.