Graph Using a Table of Values f(x) = square root of x+2-6

$f (x) = \sqrt{x + 2} - 6$

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \sqrt{(- 2) + 2} - 6$

Simplify $\sqrt{(- 2) + 2} - 6$ .

Simplify each term.

Add $- 2$ and $2$ .

$y = \sqrt{0} - 6$

Rewrite $0$ as $0^{2}$ .

$y = \sqrt{0^{2}} - 6$

Pull terms out from under the radical, assuming positive real numbers.

$y = 0 - 6$

Subtract $6$ from $0$ .

$y = - 6$

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \sqrt{(- 1) + 2} - 6$

Simplify $\sqrt{(- 1) + 2} - 6$ .

Simplify each term.

Add $- 1$ and $2$ .

$y = \sqrt{1} - 6$

Any root of $1$ is $1$ .

$y = 1 - 6$

Subtract $6$ from $1$ .

$y = - 5$

Substitute $0$ for $x$ and find the result for $y$ .

$y = \sqrt{(0) + 2} - 6$

Add $0$ and $2$ .

$y = \sqrt{2} - 6$

Substitute $1$ for $x$ and find the result for $y$ .

$y = \sqrt{(1) + 2} - 6$

Add $1$ and $2$ .

$y = \sqrt{3} - 6$

Substitute $2$ for $x$ and find the result for $y$ .

$y = \sqrt{(2) + 2} - 6$

Simplify $\sqrt{(2) + 2} - 6$ .

Simplify each term.

Add $2$ and $2$ .

$y = \sqrt{4} - 6$

Rewrite $4$ as $2^{2}$ .

$y = \sqrt{2^{2}} - 6$

Pull terms out from under the radical, assuming positive real numbers.

$y = 2 - 6$

Subtract $6$ from $2$ .

$y = - 4$

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - 6 \\ - 1 & - 5 \\ 0 & \sqrt{2} - 6 \\ 1 & \sqrt{3} - 6 \\ 2 & - 4 \end{array}$