Find the Domain and Range 2x=y^2

$2 x = y^{2}$

Rewrite the equation as $y^{2} = 2 x$ .

$y^{2} = 2 x$

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$y = \pm \sqrt{2 x}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y = \sqrt{2 x}$

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \sqrt{2 x}$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{2 x}$

$y = - \sqrt{2 x}$

$y = \sqrt{2 x}$

$y = - \sqrt{2 x}$

Set the radicand in $\sqrt{2 x}$ greater than or equal to $0$ to find where the expression is defined.

$2 x \geq 0$

Divide each term in $2 x \geq 0$ by $2$ and simplify.

Divide each term in $2 x \geq 0$ by $2$ .

$\frac{2 x}{2} \geq \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{0}{2}$

Divide $x$ by $1$ .

$x \geq \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x \geq 0$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${y | y \in ℝ}$

Determine the domain and range.

Domain: $[0, \infty), {x | x \geq 0}$

Range: $(- \infty, \infty), {y | y \in ℝ}$