1. The problem is to graph the function at the points \(\left\{-\frac{\pi}{2}, -\pi, -\frac{3\pi}{2}, -2\pi, -\frac{5\pi}{2}, -3\pi, -\frac{7\pi}{2}, 0, \frac{\pi}{2}, \pi, \frac{3\pi}{2}, 2\pi, \frac{5\pi}{2}, 3\pi, \frac{7\pi}{2}\right\}\). 2. Since the function is not explicitly given, we assume the common trigonometric function \(y=\sin x\) for these points, as these are multiples of \(\frac{\pi}{2}\). 3. The sine function formula is \(y=\sin x\). Important properties: - \(\sin 0 = 0\) - \(\sin \frac{\pi}{2} = 1\) - \(\sin \pi = 0\) - \(\sin \frac{3\pi}{2} = -1\) - \(\sin 2\pi = 0\) 4. Evaluate \(\sin x\) at each point: - \(\sin\left(-\frac{\pi}{2}\right) = -1\) - \(\sin(-\pi) = 0\) - \(\sin\left(-\frac{3\pi}{2}\right) = 1\) - \(\sin(-2\pi) = 0\) - \(\sin\left(-\frac{5\pi}{2}\right) = -1\) - \(\sin(-3\pi) = 0\) - \(\sin\left(-\frac{7\pi}{2}\right) = 1\) - \(\sin 0 = 0\) - \(\sin\frac{\pi}{2} = 1\) - \(\sin \pi = 0\) - \(\sin\frac{3\pi}{2} = -1\) - \(\sin 2\pi = 0\) - \(\sin\frac{5\pi}{2} = 1\) - \(\sin 3\pi = 0\) - \(\sin\frac{7\pi}{2} = -1\) 5. These values show the sine wave oscillates between -1 and 1 at these points. Final answer: The function values at the given points correspond to \(y=\sin x\) evaluated at those points.