Algebra Examples

$f (x) = - 3 + \frac{1}{2} \sqrt{x - 4}$

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

Add $4$ to 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:

$[- 3, \infty)$

Set-Builder Notation:

${y | y \geq - 3}$

Step 5

Determine the domain and range.

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

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

Step 6