# How do you graph y=sqrt(x-1) and how does it compare to the parent function?

Jun 20, 2018

Translate the parent graph by $1$ to the right.

#### Explanation:

The parent function is $f \left(x\right) = \sqrt{x}$, so the child function is obtained by computing $f \left(x - 1\right)$ instead of $f \left(x\right)$

This trasformation belong to the family of the horizontal translations, which happens everytime you change from $f \left(x\right)$ to $f \left(x - k\right)$.

In particular, you translate $k$ units to the left if $k > 0$, or $k$ units to the right if $k < 0$.

In this case, $k = - 1$, so this function is drawn by shifting the parent function one unit right: see below.

$f \left(x\right) = \sqrt{x}$
graph{sqrt(x) [-1, 20, -1, 5]}

$f \left(x\right) = \sqrt{x - 1}$
graph{sqrt(x-1) [-1, 20, -1, 5]}

As you can see, the two graphs are identical, except for that $1$ unit right translation.