Graph Using a Table of Values f(x) = square root of x-1

$f (x) = \sqrt{x - 1}$

Step 1

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

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

Step 2

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

Subtract $1$ 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 3

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

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

Step 4

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

Subtract $1$ from $- 1$ .

$y = \sqrt{- 2}$

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

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

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

$y = \sqrt{- 1} \cdot \sqrt{2}$

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

$y = i \sqrt{2}$

Step 5

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

$y = \sqrt{(0) - 1}$

Step 6

Simplify $\sqrt{(0) - 1}$ .

Subtract $1$ from $0$ .

$y = \sqrt{- 1}$

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

$y = i$

Step 7

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

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

Step 8

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

Subtract $1$ from $1$ .

$y = \sqrt{0}$

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

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

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

$y = 0$

Step 9

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

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

Step 10

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

Subtract $1$ from $2$ .

$y = \sqrt{1}$

Any root of $1$ is $1$ .

$y = 1$

Step 11

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

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

Step 12

Graph Using a Table of Values f(x) = square root of x-1

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