Algebra Examples

$f (x) = 3 \sqrt{x - 4}$

Step 1

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

$y = 3 \sqrt{(- 2) - 4}$

Step 2

Simplify $3 \sqrt{(- 2) - 4}$ .

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Step 2.1

Subtract $4$ from $- 2$ .

$y = 3 \sqrt{- 6}$

Step 2.2

Rewrite $- 6$ as $- 1 (6)$ .

$y = 3 \sqrt{- 1 (6)}$

Step 2.3

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$y = 3 (\sqrt{- 1} \cdot \sqrt{6})$

Step 2.4

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

$y = 3 i \sqrt{6}$

Step 3

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

$y = 3 \sqrt{(- 1) - 4}$

Step 4

Simplify $3 \sqrt{(- 1) - 4}$ .

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Step 4.1

Subtract $4$ from $- 1$ .

$y = 3 \sqrt{- 5}$

Step 4.2

Rewrite $- 5$ as $- 1 (5)$ .

$y = 3 \sqrt{- 1 (5)}$

Step 4.3

Rewrite $\sqrt{- 1 (5)}$ as $\sqrt{- 1} \cdot \sqrt{5}$ .

$y = 3 (\sqrt{- 1} \cdot \sqrt{5})$

Step 4.4

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

$y = 3 i \sqrt{5}$

Step 5

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

$y = 3 \sqrt{(0) - 4}$

Step 6

Simplify $3 \sqrt{(0) - 4}$ .

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Step 6.1

Subtract $4$ from $0$ .

$y = 3 \sqrt{- 4}$

Step 6.2

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

$y = 3 \sqrt{- 1 (4)}$

Step 6.3

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

$y = 3 (\sqrt{- 1} \cdot \sqrt{4})$

Step 6.4

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

$y = 3 (i \cdot \sqrt{4})$

Step 6.5

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

$y = 3 (i \cdot \sqrt{2^{2}})$

Step 6.6

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

$y = 3 (i \cdot 2)$

Step 6.7

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

$y = 3 (2 \cdot i)$

Step 6.8

Multiply $2$ by $3$ .

$y = 6 i$

Step 7

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

$y = 3 \sqrt{(1) - 4}$

Step 8

Simplify $3 \sqrt{(1) - 4}$ .

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Step 8.1

Subtract $4$ from $1$ .

$y = 3 \sqrt{- 3}$

Step 8.2

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

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

Step 8.3

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

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

Step 8.4

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

$y = 3 i \sqrt{3}$

Step 9

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

$y = 3 \sqrt{(2) - 4}$

Step 10

Simplify $3 \sqrt{(2) - 4}$ .

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Step 10.1

Subtract $4$ from $2$ .

$y = 3 \sqrt{- 2}$

Step 10.2

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

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

Step 10.3

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

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

Step 10.4

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

$y = 3 i \sqrt{2}$

Step 11

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

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

Step 12