Graph f(x) = square root of x^2-8

$f (x) = \sqrt{x^{2} - 8}$

Step 1

Find the $y$ value at $x = - 3$ .

Replace the variable $x$ with $- 3$ in the expression.

$f (- 3) = \sqrt{{(- 3)}^{2} - 8}$

Simplify the result.

Raise $- 3$ to the power of $2$ .

$f (- 3) = \sqrt{9 - 8}$

Subtract $8$ from $9$ .

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

Any root of $1$ is $1$ .

$f (- 3) = 1$

The final answer is $1$ .

$1$

The $y$ value at $x = - 3$ is $1$ .

$y = 1$

Step 2

Find the $y$ value at $x = - 4$ .

Replace the variable $x$ with $- 4$ in the expression.

$f (- 4) = \sqrt{{(- 4)}^{2} - 8}$

Simplify the result.

Raise $- 4$ to the power of $2$ .

$f (- 4) = \sqrt{16 - 8}$

Subtract $8$ from $16$ .

$f (- 4) = \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$f (- 4) = \sqrt{4 (2)}$

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

$f (- 4) = \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$f (- 4) = 2 \sqrt{2}$

The final answer is $2 \sqrt{2}$ .

$2 \sqrt{2}$

The $y$ value at $x = - 4$ is $2 \sqrt{2}$ .

$y = 2 \sqrt{2}$

Step 3

Find the $y$ value at $x = - 5$ .

Replace the variable $x$ with $- 5$ in the expression.

$f (- 5) = \sqrt{{(- 5)}^{2} - 8}$

Simplify the result.

Raise $- 5$ to the power of $2$ .

$f (- 5) = \sqrt{25 - 8}$

Subtract $8$ from $25$ .

$f (- 5) = \sqrt{17}$

The final answer is $\sqrt{17}$ .

$\sqrt{17}$

The $y$ value at $x = - 5$ is $\sqrt{17}$ .

$y = \sqrt{17}$

Step 4

Find the $y$ value at $x = 3$ .

Replace the variable $x$ with $3$ in the expression.

$f (3) = \sqrt{{(3)}^{2} - 8}$

Simplify the result.

Raise $3$ to the power of $2$ .

$f (3) = \sqrt{9 - 8}$

Subtract $8$ from $9$ .

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

Any root of $1$ is $1$ .

$f (3) = 1$

The final answer is $1$ .

$1$

The $y$ value at $x = 3$ is $1$ .

$y = 1$

Step 5

Find the $y$ value at $x = 4$ .

Replace the variable $x$ with $4$ in the expression.

$f (4) = \sqrt{{(4)}^{2} - 8}$

Simplify the result.

Raise $4$ to the power of $2$ .

$f (4) = \sqrt{16 - 8}$

Subtract $8$ from $16$ .

$f (4) = \sqrt{8}$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$f (4) = \sqrt{4 (2)}$

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

$f (4) = \sqrt{2^{2} \cdot 2}$

Pull terms out from under the radical.

$f (4) = 2 \sqrt{2}$

The final answer is $2 \sqrt{2}$ .

$2 \sqrt{2}$

The $y$ value at $x = 4$ is $2 \sqrt{2}$ .

$y = 2 \sqrt{2}$

Step 6

Find the $y$ value at $x = 5$ .

Replace the variable $x$ with $5$ in the expression.

$f (5) = \sqrt{{(5)}^{2} - 8}$

Simplify the result.

Raise $5$ to the power of $2$ .

$f (5) = \sqrt{25 - 8}$

Subtract $8$ from $25$ .

$f (5) = \sqrt{17}$

The final answer is $\sqrt{17}$ .

$\sqrt{17}$

The $y$ value at $x = 5$ is $\sqrt{17}$ .

$y = \sqrt{17}$

Step 7

List the points to graph.

$(- 3, 1), (- 4, 2.82842712), (- 5, 4.12310562), (3, 1), (4, 2.82842712), (5, 4.12310562)$

Step 8

Select a few points to graph.

$\begin{array}{c} x & y \\ - 5 & 4.123 \\ - 4 & 2.828 \\ - 3 & 1 \\ 3 & 1 \\ 4 & 2.828 \\ 5 & 4.123 \end{array}$

Step 9

Graph f(x) = square root of x^2-8

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