Algebra Examples

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

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

Step 1

Substitute

- 2

$- 2$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 2

Simplify

3 \sqrt{(- 2) - 4}

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

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Step 2.1

Subtract

4

$4$ from

- 2

$- 2$ .

y = 3 \sqrt{- 6}

$y = 3 \sqrt{- 6}$

Step 2.2

Rewrite

- 6

$- 6$ as

- 1 (6)

$- 1 (6)$ .

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

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

Step 2.3

Rewrite

\sqrt{- 1 (6)}

$\sqrt{- 1 (6)}$ as

\sqrt{- 1} \cdot \sqrt{6}

$\sqrt{- 1} \cdot \sqrt{6}$ .

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

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

Step 2.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

y = 3 i \sqrt{6}

$y = 3 i \sqrt{6}$

y = 3 i \sqrt{6}

$y = 3 i \sqrt{6}$

Step 3

Substitute

- 1

$- 1$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 4

Simplify

3 \sqrt{(- 1) - 4}

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

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Step 4.1

Subtract

4

$4$ from

- 1

$- 1$ .

y = 3 \sqrt{- 5}

$y = 3 \sqrt{- 5}$

Step 4.2

Rewrite

- 5

$- 5$ as

- 1 (5)

$- 1 (5)$ .

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

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

Step 4.3

Rewrite

\sqrt{- 1 (5)}

$\sqrt{- 1 (5)}$ as

\sqrt{- 1} \cdot \sqrt{5}

$\sqrt{- 1} \cdot \sqrt{5}$ .

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

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

Step 4.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

y = 3 i \sqrt{5}

$y = 3 i \sqrt{5}$

y = 3 i \sqrt{5}

$y = 3 i \sqrt{5}$

Step 5

Substitute

0

$0$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 6

Simplify

3 \sqrt{(0) - 4}

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

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Step 6.1

Subtract

4

$4$ from

0

$0$ .

y = 3 \sqrt{- 4}

$y = 3 \sqrt{- 4}$

Step 6.2

Rewrite

- 4

$- 4$ as

- 1 (4)

$- 1 (4)$ .

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

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

Step 6.3

Rewrite

\sqrt{- 1 (4)}

$\sqrt{- 1 (4)}$ as

\sqrt{- 1} \cdot \sqrt{4}

$\sqrt{- 1} \cdot \sqrt{4}$ .

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

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

Step 6.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

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

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

Step 6.5

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

y = 3 (i \cdot \sqrt{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)

$y = 3 (i \cdot 2)$

Step 6.7

Move

2

$2$ to the left of

i

$i$ .

y = 3 (2 \cdot i)

$y = 3 (2 \cdot i)$

Step 6.8

Multiply

2

$2$ by

3

$3$ .

y = 6 i

$y = 6 i$

y = 6 i

$y = 6 i$

Step 7

Substitute

1

$1$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 8

Simplify

3 \sqrt{(1) - 4}

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

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Step 8.1

Subtract

4

$4$ from

1

$1$ .

y = 3 \sqrt{- 3}

$y = 3 \sqrt{- 3}$

Step 8.2

Rewrite

- 3

$- 3$ as

- 1 (3)

$- 1 (3)$ .

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

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

Step 8.3

Rewrite

\sqrt{- 1 (3)}

$\sqrt{- 1 (3)}$ as

\sqrt{- 1} \cdot \sqrt{3}

$\sqrt{- 1} \cdot \sqrt{3}$ .

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

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

Step 8.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

y = 3 i \sqrt{3}

$y = 3 i \sqrt{3}$

y = 3 i \sqrt{3}

$y = 3 i \sqrt{3}$

Step 9

Substitute

2

$2$ for

x

$x$ and find the result for

y

$y$ .

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

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

Step 10

Simplify

3 \sqrt{(2) - 4}

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

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Step 10.1

Subtract

4

$4$ from

2

$2$ .

y = 3 \sqrt{- 2}

$y = 3 \sqrt{- 2}$

Step 10.2

Rewrite

- 2

$- 2$ as

- 1 (2)

$- 1 (2)$ .

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

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

Step 10.3

Rewrite

\sqrt{- 1 (2)}

$\sqrt{- 1 (2)}$ as

\sqrt{- 1} \cdot \sqrt{2}

$\sqrt{- 1} \cdot \sqrt{2}$ .

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

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

Step 10.4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

y = 3 i \sqrt{2}

$y = 3 i \sqrt{2}$

y = 3 i \sqrt{2}

$y = 3 i \sqrt{2}$

Step 11

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

\begin{matrix} 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{matrix}

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

Step 12