Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Add $- 2$ and $6$ .

$y = \sqrt{4}$

Step 2.2

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

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

Step 2.3

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

$y = 2$

Step 3

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

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

Step 4

Add $- 1$ and $6$ .

$y = \sqrt{5}$

Step 5

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

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

Step 6

Add $0$ and $6$ .

$y = \sqrt{6}$

Step 7

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

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

Step 8

Add $1$ and $6$ .

$y = \sqrt{7}$

Step 9

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

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

Step 10

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

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Step 10.1

Add $2$ and $6$ .

$y = \sqrt{8}$

Step 10.2

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 10.2.1

Factor $4$ out of $8$ .

$y = \sqrt{4 (2)}$

Step 10.2.2

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

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

Step 10.3

Pull terms out from under the radical.

$y = 2 \sqrt{2}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 2 \\ - 1 & \sqrt{5} \\ 0 & \sqrt{6} \\ 1 & \sqrt{7} \\ 2 & 2 \sqrt{2} \end{array}$

Step 12