Find the Domain and Range f(x)=1/2 square root of x+3

$f (x) = \frac{1}{2} \sqrt{x} + 3$

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

$x \geq 0$

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:

$[3, \infty)$

Set-Builder Notation:

${y | y \geq 3}$

Determine the domain and range.

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

Range: $[3, \infty), {y | y \geq 3}$