Algebra Examples

$f (x) = 3 \sqrt{x + 1}$

Step 1

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

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

Step 2

Simplify $3 \sqrt{(- 2) + 1}$ .

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Step 2.1

Add $- 2$ and $1$ .

$y = 3 \sqrt{- 1}$

Step 2.2

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

$y = 3 i$

Step 3

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

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

Step 4

Simplify $3 \sqrt{(- 1) + 1}$ .

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Step 4.1

Add $- 1$ and $1$ .

$y = 3 \sqrt{0}$

Step 4.2

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

$y = 3 \sqrt{0^{2}}$

Step 4.3

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

$y = 3 \cdot 0$

Step 4.4

Multiply $3$ by $0$ .

$y = 0$

Step 5

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

$y = 3 \sqrt{(0) + 1}$

Step 6

Simplify $3 \sqrt{(0) + 1}$ .

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Step 6.1

Add $0$ and $1$ .

$y = 3 \sqrt{1}$

Step 6.2

Any root of $1$ is $1$ .

$y = 3 \cdot 1$

Step 6.3

Multiply $3$ by $1$ .

$y = 3$

Step 7

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

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

Step 8

Add $1$ and $1$ .

$y = 3 \sqrt{2}$

Step 9

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

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

Step 10

Add $2$ and $1$ .

$y = 3 \sqrt{3}$

Step 11

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

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

Step 12