Algebra Examples

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

Step 1

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

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

Step 2

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

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Step 2.1

Simplify each term.

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Step 2.1.1

Add $- 2$ and $2$ .

$y = \sqrt{0} - 6$

Step 2.1.2

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

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

Step 2.1.3

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

$y = 0 - 6$

Step 2.2

Subtract $6$ from $0$ .

$y = - 6$

Step 3

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

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

Step 4

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

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Step 4.1

Simplify each term.

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Step 4.1.1

Add $- 1$ and $2$ .

$y = \sqrt{1} - 6$

Step 4.1.2

Any root of $1$ is $1$ .

$y = 1 - 6$

Step 4.2

Subtract $6$ from $1$ .

$y = - 5$

Step 5

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

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

Step 6

Add $0$ and $2$ .

$y = \sqrt{2} - 6$

Step 7

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

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

Step 8

Add $1$ and $2$ .

$y = \sqrt{3} - 6$

Step 9

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

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

Step 10

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

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Step 10.1

Simplify each term.

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Step 10.1.1

Add $2$ and $2$ .

$y = \sqrt{4} - 6$

Step 10.1.2

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

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

Step 10.1.3

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

$y = 2 - 6$

Step 10.2

Subtract $6$ from $2$ .

$y = - 4$

Step 11

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

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

Step 12