Graph y=4+1/2 square root of x+5

$y = 4 + \frac{1}{2} \sqrt{x + 5}$

Find the domain for $y = 4 + \frac{1}{2} \cdot \sqrt{x + 5}$ 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 $\sqrt{x + 5}$ greater than or equal to $0$ to find where the expression is defined.

$x + 5 \geq 0$

Subtract $5$ from both sides of the inequality.

$x \geq - 5$

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

Interval Notation:

$[- 5, \infty)$

Set-Builder Notation:

${x | x \geq - 5}$

Interval Notation:

$[- 5, \infty)$

Set-Builder Notation:

${x | x \geq - 5}$

To find the radical expression end point, substitute the $x$ value $- 5$ , which is the least value in the domain, into $f (x) = \frac{8 + \sqrt{x + 5}}{2}$ .

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

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

Simplify the result.

Simplify the numerator.

Add $- 5$ and $5$ .

$f (- 5) = \frac{8 + \sqrt{0}}{2}$

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

$f (- 5) = \frac{8 + \sqrt{0^{2}}}{2}$

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

$f (- 5) = \frac{8 + 0}{2}$

Add $8$ and $0$ .

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

Divide $8$ by $2$ .

$f (- 5) = 4$

The final answer is $4$ .

$4$

The radical expression end point is $(- 5, 4)$ .

$(- 5, 4)$

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 $- 4$ into $f (x) = \frac{8 + \sqrt{x + 5}}{2}$ . In this case, the point is $(- 4, \frac{9}{2})$ .

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

$f (- 4) = \frac{8 + \sqrt{(- 4) + 5}}{2}$

Simplify the result.

Simplify the numerator.

Add $- 4$ and $5$ .

$f (- 4) = \frac{8 + \sqrt{1}}{2}$

Any root of $1$ is $1$ .

$f (- 4) = \frac{8 + 1}{2}$

Add $8$ and $1$ .

$f (- 4) = \frac{9}{2}$

The final answer is $\frac{9}{2}$ .

$y = \frac{9}{2}$

Substitute the $x$ value $- 3$ into $f (x) = \frac{8 + \sqrt{x + 5}}{2}$ . In this case, the point is $(- 3, \frac{8 + \sqrt{2}}{2})$ .

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

$f (- 3) = \frac{8 + \sqrt{(- 3) + 5}}{2}$

Simplify the result.

Add $- 3$ and $5$ .

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

The final answer is $\frac{8 + \sqrt{2}}{2}$ .

$y = \frac{8 + \sqrt{2}}{2}$

The square root can be graphed using the points around the vertex $(- 5, 4), (- 4, 4.5), (- 3, 4.71)$

$\begin{array}{c} x & y \\ - 5 & 4 \\ - 4 & 4.5 \\ - 3 & 4.71 \end{array}$

Graph y=4+1/2 square root of x+5

Related Questions

Support LCMGCF.com by disabling your adblocker.