which is the graph of y = arctan(x)?

Explanation:

Step1: Recall properties of $y = \arctan(x)$

The function $y=\arctan(x)$ is the inverse - tangent function. Its domain is $(-\infty,\infty)$ and its range is $\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$.

Step2: Analyze end - behavior

As $x\to-\infty$, $y = \arctan(x)\to-\frac{\pi}{2}$ (but never reaches it). As $x\to\infty$, $y=\arctan(x)\to\frac{\pi}{2}$ (but never reaches it). Also, $\arctan(0) = 0$, and the function is increasing on its entire domain $(-\infty,\infty)$. The given graph satisfies all these properties.

Answer:

The provided graph is the graph of $y = \arctan(x)$.