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

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

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

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

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

Simplify each term.

Multiply $- 1$ by $- 2$ .

$y = \sqrt{2 - 2} + 2$

Subtract $2$ from $2$ .

$y = \sqrt{0} + 2$

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

$y = \sqrt{0^{2}} + 2$

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

$y = 0 + 2$

Add $0$ and $2$ .

$y = 2$

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

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

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

Simplify each term.

Multiply $- 1$ by $- 1$ .

$y = \sqrt{1 - 2} + 2$

Subtract $2$ from $1$ .

$y = \sqrt{- 1} + 2$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = i + 2$

Reorder $i$ and $2$ .

$y = 2 + i$

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

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

Simplify $\sqrt{- (0) - 2} + 2$ .

Simplify each term.

Multiply $- 1$ by $0$ .

$y = \sqrt{0 - 2} + 2$

Subtract $2$ from $0$ .

$y = \sqrt{- 2} + 2$

Rewrite $- 2$ as $- 1 (2)$ .

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

Rewrite $\sqrt{- 1 (2)}$ as $\sqrt{- 1} \cdot \sqrt{2}$ .

$y = \sqrt{- 1} \cdot \sqrt{2} + 2$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = i \sqrt{2} + 2$

Reorder $i \sqrt{2}$ and $2$ .

$y = 2 + i \sqrt{2}$

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

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

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

Simplify each term.

Multiply $- 1$ by $1$ .

$y = \sqrt{- 1 - 2} + 2$

Subtract $2$ from $- 1$ .

$y = \sqrt{- 3} + 2$

Rewrite $- 3$ as $- 1 (3)$ .

$y = \sqrt{- 1 (3)} + 2$

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$y = \sqrt{- 1} \cdot \sqrt{3} + 2$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = i \sqrt{3} + 2$

Reorder $i \sqrt{3}$ and $2$ .

$y = 2 + i \sqrt{3}$

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

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

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

Simplify each term.

Multiply $- 1$ by $2$ .

$y = \sqrt{- 2 - 2} + 2$

Subtract $2$ from $- 2$ .

$y = \sqrt{- 4} + 2$

Rewrite $- 4$ as $- 1 (4)$ .

$y = \sqrt{- 1 (4)} + 2$

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$y = \sqrt{- 1} \cdot \sqrt{4} + 2$

Rewrite $\sqrt{- 1}$ as $i$ .

$y = i \cdot \sqrt{4} + 2$

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

$y = i \cdot \sqrt{2^{2}} + 2$

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

$y = i \cdot 2 + 2$

Move $2$ to the left of $i$ .

$y = 2 i + 2$

Reorder $2 i$ and $2$ .

$y = 2 + 2 i$

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

$\begin{array}{c} x & y \\ - 2 & 2 \\ - 1 & 2 + i \\ 0 & 2 + i \sqrt{2} \\ 1 & 2 + i \sqrt{3} \\ 2 & 2 + 2 i \end{array}$

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

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