Graph y = square root of x-9

$y = \sqrt{x - 9}$

Step 1

Find the domain for $y = \sqrt{x - 9}$ 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 $\sqrt{x - 9}$ greater than or equal to $0$ to find where the expression is defined.

$x - 9 \geq 0$

Add $9$ to both sides of the inequality.

$x \geq 9$

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

Interval Notation:

$[9, \infty)$

Set-Builder Notation:

${x | x \geq 9}$

Interval Notation:

$[9, \infty)$

Set-Builder Notation:

${x | x \geq 9}$

Step 2

To find the radical expression end point, substitute the $x$ value $9$ , which is the least value in the domain, into $f (x) = \sqrt{x - 9}$ .

Replace the variable $x$ with $9$ in the expression.

$f (9) = \sqrt{(9) - 9}$

Simplify the result.

Subtract $9$ from $9$ .

$f (9) = \sqrt{0}$

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

$f (9) = \sqrt{0^{2}}$

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

$f (9) = 0$

The final answer is $0$ .

$0$

Step 3

The radical expression end point is $(9, 0)$ .

$(9, 0)$

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 $10$ into $f (x) = \sqrt{x - 9}$ . In this case, the point is $(10, 1)$ .

Replace the variable $x$ with $10$ in the expression.

$f (10) = \sqrt{(10) - 9}$

Simplify the result.

Subtract $9$ from $10$ .

$f (10) = \sqrt{1}$

Any root of $1$ is $1$ .

$f (10) = 1$

The final answer is $1$ .

$y = 1$

Substitute the $x$ value $11$ into $f (x) = \sqrt{x - 9}$ . In this case, the point is $(11, \sqrt{2})$ .

Replace the variable $x$ with $11$ in the expression.

$f (11) = \sqrt{(11) - 9}$

Simplify the result.

Subtract $9$ from $11$ .

$f (11) = \sqrt{2}$

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

$y = \sqrt{2}$

The square root can be graphed using the points around the vertex $(9, 0), (10, 1), (11, 1.41)$

$\begin{array}{c} x & y \\ 9 & 0 \\ 10 & 1 \\ 11 & 1.41 \end{array}$

Step 5

Graph y = square root of x-9

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