Find the Domain and Range f(x)=4+ square root of x-3

$f (x) = 4 + \sqrt{x - 3}$

Set the radicand in $\sqrt{x - 3}$ greater than or equal to $0$ to find where the expression is defined.

$x - 3 \geq 0$

Add $3$ to both sides of the inequality.

$x \geq 3$

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${x | x \geq 3}$

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

Interval Notation:

$[4, \infty)$

Set-Builder Notation:

${y | y \geq 4}$

Determine the domain and range.

Domain: $[3, \infty), {x | x \geq 3}$

Range: $[4, \infty), {y | y \geq 4}$