Graph Using a Table of Values f(x) = square root of x-5

$f (x) = \sqrt{x - 5}$

Step 1

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

$y = \sqrt{(- 2) - 5}$

Step 2

Simplify $\sqrt{(- 2) - 5}$ .

Subtract $5$ from $- 2$ .

$y = \sqrt{- 7}$

Rewrite $- 7$ as $- 1 (7)$ .

$y = \sqrt{- 1 (7)}$

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

$y = \sqrt{- 1} \cdot \sqrt{7}$

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

$y = i \sqrt{7}$

Step 3

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

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

Step 4

Simplify $\sqrt{(- 1) - 5}$ .

Subtract $5$ from $- 1$ .

$y = \sqrt{- 6}$

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

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

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

$y = \sqrt{- 1} \cdot \sqrt{6}$

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

$y = i \sqrt{6}$

Step 5

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

$y = \sqrt{(0) - 5}$

Step 6

Simplify $\sqrt{(0) - 5}$ .

Subtract $5$ from $0$ .

$y = \sqrt{- 5}$

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

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

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

$y = \sqrt{- 1} \cdot \sqrt{5}$

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

$y = i \sqrt{5}$

Step 7

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

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

Step 8

Simplify $\sqrt{(1) - 5}$ .

Subtract $5$ from $1$ .

$y = \sqrt{- 4}$

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

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

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

$y = \sqrt{- 1} \cdot \sqrt{4}$

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

$y = i \cdot \sqrt{4}$

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

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

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

$y = i \cdot 2$

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

$y = 2 i$

Step 9

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

$y = \sqrt{(2) - 5}$

Step 10

Simplify $\sqrt{(2) - 5}$ .

Subtract $5$ from $2$ .

$y = \sqrt{- 3}$

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

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

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

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

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

$y = i \sqrt{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & i \sqrt{7} \\ - 1 & i \sqrt{6} \\ 0 & i \sqrt{5} \\ 1 & 2 i \\ 2 & i \sqrt{3} \end{array}$

Step 12

Graph Using a Table of Values f(x) = square root of x-5

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