It looks like you uploaded an image with some questions related to the function $g(x) = 2 \sin(3x - \pi) - 5$. Let me break down the first part of the problem for you:

(a) Identify the amplitude, period, phase shift, and vertical shift.

The general form of the sine function is: $y = A \sin(Bx - C) + D$ Where:

• Amplitude is $|A|$.
• Period is $\frac{2\pi}{|B|}$.
• Phase shift is $\frac{C}{B}$.
• Vertical shift is $D$.

For the given function: $g(x) = 2 \sin(3x - \pi) - 5$

1. Amplitude: The coefficient of the sine function is $2$, so the amplitude is $|2| = 2$.

2. Period: The coefficient $B$ of $x$ inside the sine function is $3$. So, the period is: $\frac{2\pi}{|3|} = \frac{2\pi}{3}$

3. Phase shift: The phase shift is calculated using $\frac{C}{B}$. Here $C = \pi$ and $B = 3$, so: $\frac{\pi}{3}$ The phase shift is to the right by $\frac{\pi}{3}$.

4. Vertical shift: The vertical shift is $D = -5$, so the graph is shifted downward by 5 units.

Now that we have identified the amplitude, period, phase shift, and vertical shift, you can enter these values in the respective fields.

Would you like to proceed with part (b) to graph the function and identify key points? Or do you have any questions about this?