Find the Domain and Range y = square root of x-5+3

$y = \sqrt{x - 5} + 3$

Step 1

Set the radicand in $\sqrt{x - 5}$ greater than or equal to $0$ to find where the expression is defined.

$x - 5 \geq 0$

Step 2

Add $5$ to both sides of the inequality.

$x \geq 5$

Step 3

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

Interval Notation:

$[5, \infty)$

Set-Builder Notation:

${x | x \geq 5}$

Step 4

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

Interval Notation:

$[3, \infty)$

Set-Builder Notation:

${y | y \geq 3}$

Step 5

Determine the domain and range.

Domain: $[5, \infty), {x | x \geq 5}$

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

Step 6