https://file.aiquickdraw.com/mathbot/file/1725565463387ghlmw8td.jpg

The problem in the image is asking to graph the function \( h(x) = f(x) - g(x) \), where you are given two graphs of functions \( f(x) \) and \( g(x) \). 

To solve this:

1. **Interpret the Graphs of \( f(x) \) and \( g(x) \)**: Both functions are plotted in the coordinate plane. You'll need to identify the values of both functions at different points along the \( x \)-axis.

2. **Calculate \( h(x) = f(x) - g(x) \)**: For each point on the graph, subtract the value of \( g(x) \) from \( f(x) \) for the same \( x \)-value. For example, at \( x = 0 \), if \( f(0) = 2 \) and \( g(0) = -1 \), then \( h(0) = 2 - (-1) = 3 \). Repeat this for multiple values of \( x \).

3. **Plot the Points of \( h(x) \)**: After calculating \( h(x) \) at several points, you can plot these points on the same coordinate plane. Connect them to form the graph of \( h(x) \).

Would you like to proceed step by step in calculating values of \( h(x) \) for specific points, or would you prefer additional details on graphing techniques? 

### Relative questions:
1. What are the key values of \( f(x) \) and \( g(x) \) at specific points along the \( x \)-axis?
2. How does the graph of \( h(x) = f(x) - g(x) \) change compared to \( f(x) \) and \( g(x) \)?
3. Can you identify where \( h(x) \) crosses the \( x \)-axis based on the graphs of \( f(x) \) and \( g(x) \)?
4. What happens to \( h(x) \) at points where \( f(x) = g(x) \)?
5. How would the graph look if \( h(x) = f(x) + g(x) \) instead?

### Tip: 
When graphing the difference of two functions, focus on specific \( x \)-coordinates to accurately calculate and plot key points for \( h(x) \).

Use the graphs of f and g to graph h(x) = f(x) - g(x).

Learn how to graph h(x) = f(x) - g(x) using the graphs of two functions f(x) and g(x). This problem involves function subtraction and graphing techniques, suitable for students in Grades 9-12.

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