The function given is $q(x) = -2p(x+1)$, and you want to find how this transformation affects the graph of $p(x)$, which is the linear parent function.

1. Parent function: The linear parent function is $p(x) = x$.

Thus, we can rewrite $q(x)$ as: $q(x) = -2(x+1)$

Now let's break down how the graph is transformed:

• Horizontal shift: The term $(x+1)$ inside the function indicates a horizontal shift to the left by 1 unit.
• Vertical stretch and reflection: The multiplication by $-2$ outside the function represents two things:
  • A reflection across the x-axis because of the negative sign.
  • A vertical stretch by a factor of 2, meaning the graph becomes steeper.

Summary of transformations:

• Shift left by 1 unit.
• Reflect across the x-axis.
• Stretch vertically by a factor of 2.

To identify the graph:

Look for the following features in the graph:

1. The slope of the line should be steep (a slope of $-2$).
2. The line should be reflected (sloping downward instead of upward).
3. The line should be shifted to the left by 1 unit.

Do you have the graphs (A, B, C, D) available to upload? I can analyze them directly to choose the correct one.

Would you like further details on any step? If you provide the graphs, I can select the correct one.

Meanwhile, here are some related questions:

1. What happens if you shift $p(x)$ by $k$ units to the right?
2. How would a vertical compression affect the graph of $p(x)$?
3. What transformation occurs with a positive coefficient instead of $-2$?
4. Can you describe the graph of $q(x) = p(x - 3) + 2$?
5. How does a reflection across the y-axis affect a function graph?

Tip: Always consider transformations inside parentheses as horizontal shifts and outside terms as vertical changes.