Find the Domain and Range y=(x+2)^(1/4)

$y = {(x + 2)}^{\frac{1}{4}}$

Convert expressions with fractional exponents to radicals.

Apply the rule $x^{\frac{m}{n}} = \sqrt[n]{x^{m}}$ to rewrite the exponentiation as a radical.

$\sqrt[4]{{(x + 2)}^{1}}$

Anything raised to $1$ is the base itself.

$\sqrt[4]{x + 2}$

Set the radicand in $\sqrt[4]{x + 2}$ greater than or equal to $0$ to find where the expression is defined.

$x + 2 \geq 0$

Subtract $2$ from both sides of the inequality.

$x \geq - 2$

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

Interval Notation:

$[- 2, \infty)$

Set-Builder Notation:

${x | x \geq - 2}$

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Determine the domain and range.

Domain: $[- 2, \infty), {x | x \geq - 2}$

Range: $[0, \infty), {y | y \geq 0}$