Square Root Graph Parent Function

Graphing Square Root Functions

The parent function of the functions of the form $f\left(\mathrm{10}\right)=\sqrt{x-a}+b$ is $f\left(\mathrm{ten}\right)=\sqrt{x}$ .

Notation that the domain of $f\left(x\right)=\sqrt{x}$ is $x\ge 0$ and the range is $y\ge 0$ .

The graph of $f\left(x\right)=\sqrt{x-a}+b$ can exist obtained by translating the graph of $f\left(\mathrm{ten}\right)=\sqrt{x}$ to $a$ units to the right so $b$ units up.

Example:

Sketch the graph of $y=\sqrt{x-\mathrm{ane}}+2$ from its parent graph $y=\sqrt{\mathrm{10}}$ .

Solution:

Pace ane: Describe the graph of $y=\sqrt{x}$ .

Step 2: Movement the graph of $y=\sqrt{\mathrm{ten}}$ by $1$ unit to the right to obtain the graph of $y=\sqrt{x-\mathrm{ane}}$ .

Pace three: Move the graph of $y=\sqrt{x-1}$ past $2$ units upward to obtain the graph of $y=\sqrt{\mathrm{ten}-\mathrm{one}}+\mathrm{two}$ .

The domain of the function $y=\sqrt{\mathrm{10}-1}+\mathrm{ii}$ is $x\ge 1$ .

The range of the function $y=\sqrt{x-1}+2$ is $y\ge 2$ .

Square Root Graph Parent Function,

Source: https://www.varsitytutors.com/hotmath/hotmath_help/topics/graphing-square-root-functions

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