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

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

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Answer 1 · 2018-06-20T15:36:57

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

Explanation:

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

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

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

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

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

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

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

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

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