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

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

Step 1

Set the radicand in $\sqrt{x - 1 + 4}$ greater than or equal to $0$ to find where the expression is defined.

$x - 1 + 4 \geq 0$

Step 2

Solve for $x$ .

Add $- 1$ and $4$ .

$x + 3 \geq 0$

Subtract $3$ from both sides of the inequality.

$x \geq - 3$

Step 3

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

Interval Notation:

$[- 3, \infty)$

Set-Builder Notation:

${x | x \geq - 3}$

Step 4

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

Interval Notation:

$(- \infty, 0]$

Set-Builder Notation:

${y | y \leq 0}$

Step 5

Determine the domain and range.

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

Range: $(- \infty, 0], {y | y \leq 0}$

Step 6