The equation of a curve is $y = 4 - 3\cos 2x$.

1. Determine the amplitude of the function

The amplitude is given by the absolute value of the coefficient of the cosine term.
Amplitude $= |-3| = 3$

2. Determine the period of the function

The period of $\cos(bx)$ is $\frac{2\pi}{b}$. Here, $b = 2$.
Period $= \frac{2\pi}{2} = \pi$

1. Identify the key features of the graph from the equation

The equation is $y = 4 - 3\cos 2x$.
Principal axis: $y = 4$
Amplitude: $3$
Maximum value: $4 + 3 = 7$
Minimum value: $4 - 3 = 1$
Period: $\frac{2\pi}{2} = \pi$

2. Determine the key points for the given domain $0 \le x \le 2\pi$

Since the period is $\pi$, there are two full cycles in the domain $0 \le x \le 2\pi$.
Key points for the first cycle:

• Minimum at $x = 0$: $(0, 1)$
• Crosses principal axis at $x = \frac{\pi}{4}$: $(\frac{\pi}{4}, 4)$
• Maximum at $x = \frac{\pi}{2}$: $(\frac{\pi}{2}, 7)$
• Crosses principal axis at $x = \frac{3\pi}{4}$: $(\frac{3\pi}{4}, 4)$
• Minimum at $x = \pi$: $(\pi, 1)$

Key points for the second cycle:

• Crosses principal axis at $x = \frac{5\pi}{4}$: $(\frac{5\pi}{4}, 4)$
• Maximum at $x = \frac{3\pi}{2}$: $(\frac{3\pi}{2}, 7)$
• Crosses principal axis at $x = \frac{7\pi}{4}$: $(\frac{7\pi}{4}, 4)$
• Minimum at $x = 2\pi$: $(2\pi, 1)$

3. Sketch the graph

Draw a smooth, inverted cosine curve passing through the identified key points, ensuring the shape is symmetric and the turning points are rounded.