Graph y=1/2 square root of x+2

$y = \frac{1}{2} \sqrt{x + 2}$

Find the domain for $y = \frac{1}{2} \cdot \sqrt{x + 2}$ 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 $\sqrt{x + 2}$ greater than or equal to $0$ to find where the expression is defined.

$x + 2 \geq 0$

Subtract $2$ from both sides of the inequality.

$x \geq - 2$

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

Interval Notation:

$[- 2, \infty)$

Set-Builder Notation:

${x | x \geq - 2}$

Interval Notation:

$[- 2, \infty)$

Set-Builder Notation:

${x | x \geq - 2}$

To find the radical expression end point, substitute the $x$ value $- 2$ , which is the least value in the domain, into $f (x) = \frac{\sqrt{x + 2}}{2}$ .

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

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

Simplify the result.

Simplify the numerator.

Add $- 2$ and $2$ .

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

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

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

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

$f (- 2) = \frac{0}{2}$

Divide $0$ by $2$ .

$f (- 2) = 0$

The final answer is $0$ .

$0$

The radical expression end point is $(- 2, 0)$ .

$(- 2, 0)$

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

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

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

Simplify the result.

Simplify the numerator.

Add $- 1$ and $2$ .

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

Any root of $1$ is $1$ .

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

The final answer is $\frac{1}{2}$ .

$y = \frac{1}{2}$

Substitute the $x$ value $0$ into $f (x) = \frac{\sqrt{x + 2}}{2}$ . In this case, the point is $(0, \frac{\sqrt{2}}{2})$ .

Replace the variable $x$ with $0$ in the expression.

$f (0) = \frac{\sqrt{(0) + 2}}{2}$

Simplify the result.

Add $0$ and $2$ .

$f (0) = \frac{\sqrt{2}}{2}$

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

$y = \frac{\sqrt{2}}{2}$

The square root can be graphed using the points around the vertex $(- 2, 0), (- 1, 0.5), (0, 0.71)$

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & 0.5 \\ 0 & 0.71 \end{array}$

Graph y=1/2 square root of x+2

Related Questions

Support LCMGCF.com by disabling your adblocker.