The image shows a question asking to graph the function:

$2 \cdot f(x+2) - 1$

Here's the breakdown of this transformation based on the function $f(x)$:

1. Horizontal Shift: The expression $f(x + 2)$ shifts the graph of $f(x)$ to the left by 2 units.
2. Vertical Scaling: The coefficient 2 in front of $f(x + 2)$ vertically stretches the graph, meaning all the $y$-values will be doubled.
3. Vertical Shift: The $-1$ at the end shifts the graph downward by 1 unit.

So, to graph $2 \cdot f(x+2) - 1$, follow these steps:

1. Start with the graph of $f(x)$: Identify the original graph of $f(x)$.
2. Apply the horizontal shift: Move every point of $f(x)$ 2 units to the left.
3. Apply the vertical scaling: Double the $y$-coordinates of each point from the shifted graph.
4. Apply the vertical shift: Finally, subtract 1 from each $y$-coordinate to shift the graph down.

If you'd like further guidance on how to plot these transformations or have any questions about the steps, feel free to ask!

Would you like more details on any of these transformations? Here are five related questions that may help you further understand the process:

1. How does the horizontal shift affect different types of functions (linear, quadratic, etc.)?
2. What happens if the scaling factor (here 2) is negative?
3. How do you graph vertical stretches and compressions for trigonometric functions?
4. Can you explain how combining transformations can change the appearance of a polynomial graph?
5. What is the significance of the order of applying these transformations?

Tip: When performing multiple transformations, always apply horizontal shifts and stretches first, followed by vertical adjustments.