Question

the function $f(x) = \sqrt{x} - 3$ is graphed on the coordinate grid.
which inequality describes the range of $f(x)$?
$\bigcirc$ $y \geq -5$
$\bigcirc$ $y \geq -3$
$\bigcirc$ $y \geq 0$
$\bigcirc$ $y \geq 3$

Explanation:

Step1: Identify base function range

The square root function $\sqrt{x}$ has a range of $\sqrt{x} \geq 0$ for all valid $x \geq 0$.

Step2: Apply vertical transformation

Subtract 3 from the base function: $f(x) = \sqrt{x} - 3$. This shifts the entire range down by 3 units.
<Expression>
$\sqrt{x} - 3 \geq 0 - 3$
</Expression>

Step3: Simplify to find final range

Simplify the inequality to get the range of $f(x)$.
<Expression>
$f(x) \geq -3$ or $y \geq -3$
</Expression>

Answer:

B. $y \geq -3$