1. **Problem Statement:** Find the range, amplitude, and period of the function $$y = \cos x - 5$$ and understand its graph. 2. **Recall the cosine function properties:** - The standard cosine function $$y = \cos x$$ has a range of $$[-1, 1]$$. - The amplitude is the distance from the midline to a peak, which is $$1$$ for $$\cos x$$. - The period is the length of one full cycle, which is $$360^\circ$$ or $$2\pi$$ radians. 3. **Effect of vertical shift:** - The function $$y = \cos x - 5$$ shifts the graph of $$\cos x$$ down by 5 units. - This means the range shifts from $$[-1, 1]$$ to $$[-1-5, 1-5] = [-6, -4]$$. 4. **Amplitude:** - Amplitude is the absolute value of the coefficient before $$\cos x$$, which is $$1$$ here. 5. **Period:** - Since there is no horizontal stretch or compression, the period remains $$360^\circ$$. **Final answers:** - Range: $$[-6, -4]$$ - Amplitude: $$1$$ - Period: $$360^\circ$$