https://file.aiquickdraw.com/mathbot/file/1725767776756p53xga7t.jpg

It looks like the image presents two functions, \( f(x) \) and \( g(x) \), along with the graph of their sum \( (f + g)(x) \). The task is to position points \( A \) and \( B \) on the graph such that they both lie on the graph of \( (f + g)(x) \).

Let me guide you through this:

1. **Graph of \( (f + g)(x) \)**: The graph of \( f(x) + g(x) \) is obtained by adding the \( y \)-coordinates of the functions \( f(x) \) and \( g(x) \) for each \( x \)-value. You would look for the points on the graph where the sum of their \( y \)-coordinates match the values of \( A \) and \( B \).

2. **Positioning of Points \( A \) and \( B \)**: The coordinates of these points need to satisfy the equation of \( (f + g)(x) \). By visually identifying the graph of \( f(x) \) and \( g(x) \), you can then find the points where their sum matches the positions of \( A \) and \( B \).

Would you like me to calculate or explain how to find exact points for \( A \) and \( B \)? If you'd prefer, I can walk you through the detailed steps of how to analyze this situation.

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Here are five questions related to this:

1. How do you calculate the point-wise sum of two functions on a graph?
2. What are the key visual differences between the graphs of \( f(x) \) and \( g(x) \) in this image?
3. How does the behavior of \( f(x) + g(x) \) change compared to \( f(x) \) and \( g(x) \)?
4. What specific coordinates would you choose for \( A \) and \( B \) to match the graph of \( (f + g)(x) \)?
5. How can you algebraically verify that points \( A \) and \( B \) lie on the graph of \( (f + g)(x) \)?

**Tip**: When adding two functions graphically, always align their corresponding \( x \)-values and sum their \( y \)-values.

Position points A and B so they both lie on the graph of (f + g)(x).

Learn how to position points A and B on the graph of (f + g)(x) using function addition. This example explains graph analysis and function point-wise addition for students in Grades 9-11.

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