Question

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

Answer 1

`color(red)(y_x=sqrt(2-x))` is the parent function `color(green)(y_(barx)=sqrt(-barx))` shifted 2 units to the right,
which, in turn, is its parent function `color(purple)(y_(hatx)=sqrt(hatx))` reflected through the Y-axis

Explanation:

Note that `color(purple)(hatx)` is the same as `color(green)((-barx))` except that all `color(purple)(hatx)` values are the negative of their corresponding `color(green)(barx)` values. That is `color(green)(-barx)` is the reflection of `color(purple)(hatx)` through the Y-axis.

`color(red)(2-x)` takes every value `color(green)(barx)` and increases it by `color(red)2`, effectively shifting all points 2 units to the right.

Provided you know how to draw `color(purple)y_(hatx)=sqrt(hatx)`
graphing this function should be straight forward if you just perform the reflection and shift.