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

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

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Answer 1 · 2017-11-01T11:09:17

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

Explanation:

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

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

Provided you know how to draw $y_{ˆ x} = \sqrt{ˆ x}$ $color(purple)y_(hatx)=sqrt(hatx)$
graphing this function should be straight forward if you just perform the reflection and shift.
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How do you graph $y = \sqrt{2 - x}$ $y=sqrt(2-x$ and how does it compare to the parent function?

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

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