Negative Cosine F1F4B3

1. **State the problem:** We are given the function $$y = -3 \cos x$$ and want to understand its properties. 2. **Recall the cosine function:** The basic cosine function $$\cos x$$ oscillates between $$-1$$ and $$1$$. 3. **Apply the amplitude:** Multiplying by $$-3$$ scales the amplitude to $$3$$ and reflects the graph across the x-axis. 4. **Range of the function:** Since $$\cos x$$ ranges from $$-1$$ to $$1$$, $$-3 \cos x$$ ranges from $$-3 \times 1 = -3$$ to $$-3 \times (-1) = 3$$. 5. **Summary:** The function $$y = -3 \cos x$$ oscillates between $$-3$$ and $$3$$ with a period of $$2\pi$$ and is reflected vertically compared to $$y = 3 \cos x$$.