1. **Problem Statement:** Identify the graph described, which resembles the tangent function over the interval $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$. 2. **Formula and Important Rules:** The tangent function is defined as $$y = \tan(x) = \frac{\sin(x)}{\cos(x)}$$. - It has vertical asymptotes where $$\cos(x) = 0$$, which occur at $$x = \pm \frac{\pi}{2}$$ within the given interval. - The function crosses the x-axis where $$\sin(x) = 0$$, which is at $$x=0$$. - The tangent function is odd and periodic with period $$\pi$$. 3. **Intermediate Work and Explanation:** - The graph starts below the x-axis on the left side near $$-\frac{\pi}{2}$$, indicating the function approaches negative infinity as $$x \to -\frac{\pi}{2}^+$$. - It crosses the x-axis at $$x=0$$. - It sharply rises upward after $$\frac{\pi}{4}$$, passing through points approximately at $$y=1$$ and above, consistent with $$\tan(x)$$ increasing to positive infinity as $$x \to \frac{\pi}{2}^-$$. 4. **Conclusion:** The graph is the function $$y = \tan(x)$$ over the interval $$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$. **Final answer:** $$y = \tan(x)$$