1. The problem is to analyze the function $y = \cos x$ and understand its key features including intercepts and extrema. 2. The cosine function has the form $y = \cos x$, which is periodic with period $2\pi$ and amplitude 1. 3. To find x-intercepts, solve $\cos x = 0$. This occurs at $x = \frac{\pi}{2} + n\pi$ for integers $n$. 4. To find extrema, compute derivative $y' = -\sin x$ and set $y' = 0$ to find critical points at $x = n\pi$. 5. At $x = 2n\pi$, $\cos x = 1$, which are local maxima. 6. At $x = (2n+1)\pi$, $\cos x = -1$, which are local minima. 7. Points A and B mentioned correspond to an x-intercept at $x = -\frac{\pi}{2}$ (A) and a minimum at $x = -\pi$ (B). 8. Summary: The graph of $y = \cos x$ oscillates between 1 and -1 with zeros at $\frac{\pi}{2} + n\pi$ and extrema at multiples of $\pi$.