From the image provided, here is the information extracted and analyzed:

1. Amplitude and Period (Question a, part i):

   • The equation provided for the graph is $y = 3 \cos(2x) - 1$.
   • Amplitude: The amplitude of a cosine function $y = A \cos(Bx) + C$ is given by the absolute value of $A$. Here, $A = 3$, so the amplitude is 3.
   • Period: The period of a cosine function is calculated as $\frac{2\pi}{B}$. Here, $B = 2$, so the period $= \frac{2\pi}{2} = \pi$. In degrees, this is equivalent to $180^\circ$, so the period is 2 (in terms of the problem, this likely represents a simplified unit).

2. Graph (Question ii):

   • The function $y = 3 \cos(2x) - 1$ is graphed on the $y$-axis against the $x$-axis.
   • Key points at each quarter cycle (90°, 180°, 270°, 360°) are marked, showing the oscillation from a maximum of 2 to a minimum of -4.
   • The phase shift and vertical shift (downward by 1 unit due to "-1") are applied.

Would you like a step-by-step breakdown of the graph characteristics or other parts of the question?

Additional Questions to Explore:

1. How does changing the amplitude affect the shape of a cosine graph?
2. What impact does adjusting the period have on the cosine function's frequency?
3. How would a phase shift (e.g., $y = 3 \cos(2x - \frac{\pi}{4})$) affect the graph?
4. What happens if a sine function is used instead of cosine, keeping amplitude and period the same?
5. How is the graph affected by altering the vertical shift (e.g., $y = 3 \cos(2x) + 2$)?

Tip: Remember that amplitude affects the "height" of peaks and troughs, while period determines the "width" or frequency of cycles.