Find the Domain and Range y=- square root of 2x-5

$y = - \sqrt{2 x - 5}$

Step 1

Set the radicand in $\sqrt{2 x - 5}$ greater than or equal to $0$ to find where the expression is defined.

$2 x - 5 \geq 0$

Step 2

Solve for $x$ .

Add $5$ to both sides of the inequality.

$2 x \geq 5$

Divide each term in $2 x \geq 5$ by $2$ and simplify.

Divide each term in $2 x \geq 5$ by $2$ .

$\frac{2 x}{2} \geq \frac{5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{5}{2}$

Divide $x$ by $1$ .

$x \geq \frac{5}{2}$

Step 3

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

Interval Notation:

$[\frac{5}{2}, \infty)$

Set-Builder Notation:

${x | x \geq \frac{5}{2}}$

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: $[\frac{5}{2}, \infty), {x | x \geq \frac{5}{2}}$

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

Step 6