Graph f(x,y) = square root of 2x-y

$f (x, y) = \sqrt{2 x - y}$

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

$2 x - y \geq 0$

Solve for $x$ .

Add $y$ to both sides of the inequality.

$2 x \geq y$

Divide each term in $2 x \geq y$ by $2$ and simplify.

Divide each term in $2 x \geq y$ by $2$ .

$\frac{2 x}{2} \geq \frac{y}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{y}{2}$

Divide $x$ by $1$ .

$x \geq \frac{y}{2}$

The domain is all real numbers.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

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

Replace the variable $x$ with $x E R$ in the expression.

$f (x E R) = \sqrt{2 (x E R) - y}$

Simplify the result.

Remove parentheses.

$f (x E R) = \sqrt{2 x E R - y}$

The final answer is $\sqrt{2 x E R - y}$ .

$\sqrt{2 x E R - y}$

The radical expression end point is $(x E R, \sqrt{2 x E R - y})$ .

$(x E R, \sqrt{2 x E R - y})$

The square root can be graphed using the points around the vertex $(x E R, \sqrt{2 x E R - y}),$

$\begin{array}{c} x & y \\ x E R & \sqrt{2 x E R - y} \end{array}$