Find the Domain and Range y=- square root of x+4-1

$y = - \sqrt{x + 4} - 1$

Step 1

Set the radicand in $\sqrt{x + 4}$ greater than or equal to $0$ to find where the expression is defined.

$x + 4 \geq 0$

Step 2

Subtract $4$ from both sides of the inequality.

$x \geq - 4$

Step 3

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

Interval Notation:

$[- 4, \infty)$

Set-Builder Notation:

${x | x \geq - 4}$

Step 4

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

Interval Notation:

$(- \infty, - 1]$

Set-Builder Notation:

${y | y \leq - 1}$

Step 5

Determine the domain and range.

Domain: $[- 4, \infty), {x | x \geq - 4}$

Range: $(- \infty, - 1], {y | y \leq - 1}$

Step 6