Question

which is the graph of $f(x) = \sqrt{x}$?

Explanation:

Step1: Define domain of $f(x)=\sqrt{x}$

The square root function $\sqrt{x}$ is only defined for non-negative real numbers, so $x \geq 0$.

Step2: Analyze function behavior

For $x=0$, $f(0)=\sqrt{0}=0$. As $x$ increases, $f(x)=\sqrt{x}$ increases at a decreasing rate (curves upward, not steepening like a parabola). The top graph is $y=x^2$ (defined for all $x$, symmetric over y-axis), which does not match.

Step3: Match to correct graph

The bottom graph has a domain $x \geq 0$, passes through $(0,0)$, and has the slow-increasing curve of a square root function.

Answer:

The bottom graph (the second option, starting at the origin and curving upward in the first quadrant) is the graph of $f(x)=\sqrt{x}$.