Find the Domain and Range square root of 12+x

$\sqrt{12 + x}$

Step 1

Set the radicand in $\sqrt{12 + x}$ greater than or equal to $0$ to find where the expression is defined.

$12 + x \geq 0$

Step 2

Subtract $12$ from both sides of the inequality.

$x \geq - 12$

Step 3

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

Interval Notation:

$[- 12, \infty)$

Set-Builder Notation:

${x | x \geq - 12}$

Step 4

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

Interval Notation:

$[0, \infty)$

Set-Builder Notation:

${y | y \geq 0}$

Step 5

Determine the domain and range.

Domain: $[- 12, \infty), {x | x \geq - 12}$

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

Step 6