Find the Domain and Range y=-x^(1/2)+5

$y = - x^{\frac{1}{2}} + 5$

Step 1

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.

$- \sqrt{x^{1}} + 5$

Anything raised to $1$ is the base itself.

$- \sqrt{x} + 5$

Step 2

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

$x \geq 0$

Step 3

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${x | x \geq 0}$

Step 4

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

Interval Notation:

$(- \infty, 5]$

Set-Builder Notation:

${y | y \leq 5}$

Step 5

Determine the domain and range.

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

Range: $(- \infty, 5], {y | y \leq 5}$

Step 6