Graph y=1/2 square root of x+3-2

$y = \frac{1}{2} \sqrt{x + 3} - 2$

Find the domain for $y = \frac{1}{2} \cdot \sqrt{x + 3} - 2$ 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 $\sqrt{x + 3}$ 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:

${x | x \geq - 3}$

To find the radical expression end point, substitute the $x$ value $- 3$ , which is the least value in the domain, into $f (x) = \frac{\sqrt{x + 3} - 4}{2}$ .

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

$f (- 3) = \frac{\sqrt{(- 3) + 3} - 4}{2}$

Simplify the result.

Simplify the numerator.

Add $- 3$ and $3$ .

$f (- 3) = \frac{\sqrt{0} - 4}{2}$

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

$f (- 3) = \frac{\sqrt{0^{2}} - 4}{2}$

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

$f (- 3) = \frac{0 - 4}{2}$

Subtract $4$ from $0$ .

$f (- 3) = \frac{- 4}{2}$

Divide $- 4$ by $2$ .

$f (- 3) = - 2$

The final answer is $- 2$ .

$- 2$

The radical expression end point is $(- 3, - 2)$ .

$(- 3, - 2)$

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 $f (x) = \frac{\sqrt{x + 3} - 4}{2}$ . In this case, the point is $(- 2, - \frac{3}{2})$ .

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

$f (- 2) = \frac{\sqrt{(- 2) + 3} - 4}{2}$

Simplify the result.

Simplify the numerator.

Add $- 2$ and $3$ .

$f (- 2) = \frac{\sqrt{1} - 4}{2}$

Any root of $1$ is $1$ .

$f (- 2) = \frac{1 - 4}{2}$

Subtract $4$ from $1$ .

$f (- 2) = \frac{- 3}{2}$

Move the negative in front of the fraction.

$f (- 2) = - \frac{3}{2}$

The final answer is $- \frac{3}{2}$ .

$y = - \frac{3}{2}$

Substitute the $x$ value $- 1$ into $f (x) = \frac{\sqrt{x + 3} - 4}{2}$ . In this case, the point is $(- 1, \frac{\sqrt{2} - 4}{2})$ .

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

$f (- 1) = \frac{\sqrt{(- 1) + 3} - 4}{2}$

Simplify the result.

Add $- 1$ and $3$ .

$f (- 1) = \frac{\sqrt{2} - 4}{2}$

The final answer is $\frac{\sqrt{2} - 4}{2}$ .

$y = \frac{\sqrt{2} - 4}{2}$

The square root can be graphed using the points around the vertex $(- 3, - 2), (- 2, - 1.5), (- 1, - 1.29)$

$\begin{array}{c} x & y \\ - 3 & - 2 \\ - 2 & - 1.5 \\ - 1 & - 1.29 \end{array}$

Graph y=1/2 square root of x+3-2

Related Questions

Support LCMGCF.com by disabling your adblocker.