Let's break down how to solve each part of the problem:

Part (a): $y = 2f(x - 3)$

1. Horizontal Shift: The transformation $f(x - 3)$ means a shift to the right by 3 units. So, we move the graph of $f(x)$ three units to the right.
2. Vertical Stretch: The multiplication by 2, $2f(x - 3)$, means the graph will stretch vertically by a factor of 2. Every y-coordinate on the graph will be multiplied by 2.

To summarize:

• Move the graph of $f(x)$ right by 3 units.
• Multiply all y-values by 2 to stretch the graph vertically.

Part (b): $y = h(-x) - 1$

1. Horizontal Reflection: The transformation $h(-x)$ reflects the graph across the y-axis. So, the graph will flip horizontally.
2. Vertical Shift: The subtraction of 1, $h(-x) - 1$, shifts the graph down by 1 unit. Every point on the graph will move down 1 unit.

To summarize:

• Reflect the graph of $h(x)$ across the y-axis.
• Move the entire graph down by 1 unit.

Would you like further details or examples for this? Here are five related questions you might want to consider:

1. How do different transformations (like reflections and stretches) affect the domain and range of a function?
2. Can vertical and horizontal transformations change the overall shape of the graph?
3. What happens if we have a combination of multiple transformations?
4. How would the transformations be different if we had $f(2x)$ instead of $2f(x)$?
5. Can these transformations affect symmetry properties of a function?

Tip: Always apply horizontal transformations (like shifts and reflections) before vertical ones, when multiple transformations are present!