The question asks to "Choose the correct graph" of the function $y = \cos x$. Let's analyze the provided graphs:

The cosine function, $y = \cos x$, has the following characteristics:

• Period: $2\pi$
• Amplitude: 1 (meaning the graph oscillates between 1 and -1)
• Key points: At $x = 0$, $\cos(0) = 1$; at $x = \frac{\pi}{2}$, $\cos\left(\frac{\pi}{2}\right) = 0$; at $x = \pi$, $\cos(\pi) = -1$; and it continues this oscillating behavior between $-1$ and $1$.

Identifying the correct graph:

Looking at the options, option C matches the expected shape of the cosine function:

• The graph starts at $y = 1$ when $x = 0$.
• It crosses the x-axis at $x = \frac{\pi}{2}$.
• It reaches a minimum value of $y = -1$ at $x = \pi$.
• It follows the correct oscillation pattern within the range $0 \leq x \leq 2\pi$.

Therefore, C is the correct answer.

Would you like more details about the cosine function, or do you have any further questions?

Here are 5 related questions to deepen your understanding:

1. What is the amplitude and period of $y = \sin x$ compared to $y = \cos x$?
2. How does the phase shift affect the graph of a cosine function?
3. What would the graph of $y = \cos(2x)$ look like compared to $y = \cos x$?
4. How can the graph of $y = \cos x$ be translated vertically?
5. What is the relationship between the graphs of $y = \sin x$ and $y = \cos x$?

Tip: The graph of $y = \cos x$ is periodic, meaning it repeats its shape every $2\pi$. Understanding this periodicity helps in recognizing transformations and translations of trigonometric functions.