# How do you graph y=sqrt(2-x and how does it compare to the parent function?

Nov 1, 2017

$\textcolor{red}{{y}_{x} = \sqrt{2 - x}}$ is the parent function $\textcolor{g r e e n}{{y}_{\overline{x}} = \sqrt{- \overline{x}}}$ shifted 2 units to the right,
which, in turn, is its parent function $\textcolor{p u r p \le}{{y}_{\hat{x}} = \sqrt{\hat{x}}}$ reflected through the Y-axis

#### Explanation:

Note that $\textcolor{p u r p \le}{\hat{x}}$ is the same as $\textcolor{g r e e n}{\left(- \overline{x}\right)}$ except that all $\textcolor{p u r p \le}{\hat{x}}$ values are the negative of their corresponding $\textcolor{g r e e n}{\overline{x}}$ values. That is $\textcolor{g r e e n}{- \overline{x}}$ is the reflection of $\textcolor{p u r p \le}{\hat{x}}$ through the Y-axis.

$\textcolor{red}{2 - x}$ takes every value $\textcolor{g r e e n}{\overline{x}}$ and increases it by $\textcolor{red}{2}$, effectively shifting all points 2 units to the right.

Provided you know how to draw ${\textcolor{p u r p \le}{y}}_{\hat{x}} = \sqrt{\hat{x}}$
graphing this function should be straight forward if you just perform the reflection and shift. 