Graph y = square root of x+6

$y = \sqrt{x + 6}$

Step 1

Find the domain for $y = \sqrt{x + 6}$ so that a list of $x$ values can be picked to find a list of points, which will help graphing the radical.

Set the radicand in $\sqrt{x + 6}$ greater than or equal to $0$ to find where the expression is defined.

$x + 6 \geq 0$

Subtract $6$ from both sides of the inequality.

$x \geq - 6$

The domain is all values of $x$ that make the expression defined.

Interval Notation:

$[- 6, \infty)$

Set-Builder Notation:

${x | x \geq - 6}$

Interval Notation:

$[- 6, \infty)$

Set-Builder Notation:

${x | x \geq - 6}$

Step 2

To find the radical expression end point, substitute the $x$ value $- 6$ , which is the least value in the domain, into $f (x) = \sqrt{x + 6}$ .

Replace the variable $x$ with $- 6$ in the expression.

$f (- 6) = \sqrt{(- 6) + 6}$

Simplify the result.

Add $- 6$ and $6$ .

$f (- 6) = \sqrt{0}$

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

$f (- 6) = \sqrt{0^{2}}$

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

$f (- 6) = 0$

The final answer is $0$ .

$0$

Step 3

The radical expression end point is $(- 6, 0)$ .

$(- 6, 0)$

Step 4

Select a few $x$ values from the domain. It would be more useful to select the values so that they are next to the $x$ value of the radical expression end point.

Substitute the $x$ value $- 5$ into $f (x) = \sqrt{x + 6}$ . In this case, the point is $(- 5, 1)$ .

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

$f (- 5) = \sqrt{(- 5) + 6}$

Simplify the result.

Add $- 5$ and $6$ .

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

Any root of $1$ is $1$ .

$f (- 5) = 1$

The final answer is $1$ .

$y = 1$

Substitute the $x$ value $- 4$ into $f (x) = \sqrt{x + 6}$ . In this case, the point is $(- 4, \sqrt{2})$ .

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

$f (- 4) = \sqrt{(- 4) + 6}$

Simplify the result.

Add $- 4$ and $6$ .

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

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

$y = \sqrt{2}$

The square root can be graphed using the points around the vertex $(- 6, 0), (- 5, 1), (- 4, 1.41)$

$\begin{array}{c} x & y \\ - 6 & 0 \\ - 5 & 1 \\ - 4 & 1.41 \end{array}$

Step 5

Graph y = square root of x+6

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