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

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

Step 1

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

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

Step 2

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

Remove parentheses.

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

Simplify each term.

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 $2$ .

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

Step 3

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

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

Step 4

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

Remove parentheses.

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

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

$y = i + 2$

Reorder $i$ and $2$ .

$y = 2 + i$

Step 5

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

$y = \sqrt{0} + 2$

Step 6

Simplify $\sqrt{0} + 2$ .

Remove parentheses.

$y = \sqrt{0} + 2$

Simplify each term.

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 $2$ .

$y = 2$

Step 7

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

$y = \sqrt{1} + 2$

Step 8

Simplify $\sqrt{1} + 2$ .

Remove parentheses.

$y = \sqrt{1} + 2$

Any root of $1$ is $1$ .

$y = 1 + 2$

Add $1$ and $2$ .

$y = 3$

Step 9

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

$y = \sqrt{2} + 2$

Step 10

Remove parentheses.

$y = \sqrt{2} + 2$

Step 11

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

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

Step 12

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

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