which of the following graphs is the correct plot of $y = -4 \\cos(x)$?

Explanation:

Step1: Identify the y-intercept

Evaluate the function at $x = 0$. $$y = -4 \cos(0) = -4(1) = -4$$

Step2: Determine the amplitude

The coefficient $-4$ indicates an amplitude of $4$. $$|A| = |-4| = 4$$

Step3: Check the period

The period of $\cos(x)$ is $2\pi$, approximately $6.28$. $$T = 2\pi \approx 6.28$$

Step4: Match with the graphs

The first graph starts at $(0, -4)$, peaks at $x \approx 3.14$, and returns to $-4$ at $x \approx 6.28$.

Answer:

The first graph (top-left) is the correct plot.