Graph y=- square root of x+3

$y = - \sqrt{x + 3}$

Step 1

Find the domain for $y = - \sqrt{x + 3}$ 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 $\sqrt{x + 3}$ greater than or equal to $0$ to find where the expression is defined.

$x + 3 \geq 0$

Subtract $3$ from both sides of the inequality.

$x \geq - 3$

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

Interval Notation:

$[- 3, \infty)$

Set-Builder Notation:

${x | x \geq - 3}$

Interval Notation:

$[- 3, \infty)$

Set-Builder Notation:

${x | x \geq - 3}$

Step 2

To find the radical expression end point, substitute the $x$ value $- 3$ , which is the least value in the domain, into $f (x) = - \sqrt{x + 3}$ .

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

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

Simplify the result.

Add $- 3$ and $3$ .

$f (- 3) = - \sqrt{0}$

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

$f (- 3) = - \sqrt{0^{2}}$

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

$f (- 3) = - 0$

Multiply $- 1$ by $0$ .

$f (- 3) = 0$

The final answer is $0$ .

$0$

Step 3

The radical expression end point is $(- 3, 0)$ .

$(- 3, 0)$

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 $- 2$ into $f (x) = - \sqrt{x + 3}$ . In this case, the point is $(- 2, - 1)$ .

Replace the variable $x$ with $- 2$ in the expression.

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

Simplify the result.

Add $- 2$ and $3$ .

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

Any root of $1$ is $1$ .

$f (- 2) = - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$f (- 2) = - 1$

The final answer is $- 1$ .

$y = - 1$

Substitute the $x$ value $- 1$ into $f (x) = - \sqrt{x + 3}$ . In this case, the point is $(- 1, - \sqrt{2})$ .

Replace the variable $x$ with $- 1$ in the expression.

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

Simplify the result.

Add $- 1$ and $3$ .

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

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

$y = - \sqrt{2}$

The square root can be graphed using the points around the vertex $(- 3, 0), (- 2, - 1), (- 1, - 1.41)$

$\begin{array}{c} x & y \\ - 3 & 0 \\ - 2 & - 1 \\ - 1 & - 1.41 \end{array}$

Step 5

Graph y=- square root of x+3

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