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To find the domain of \( f + g \), we need to identify where both functions \( f(x) \) (in blue) and \( g(x) \) (in red) are defined on the graph. The domain of \( f + g \) will be the overlap of the domains of both functions.

From the graph, we can observe the following:

- The domain of \( f(x) \) is from \( x = -6 \) to \( x = 3 \), as these are the points where the function is defined.
- The domain of \( g(x) \) is from \( x = -5 \) to \( x = 6 \), as these are the points where \( g(x) \) is defined.

The domain of \( f + g \) is the intersection (overlap) of the domains of \( f(x) \) and \( g(x) \). Therefore, the domain of \( f + g \) is the interval where both functions exist simultaneously, which is from \( x = -5 \) to \( x = 3 \).

So, the domain of \( f + g \) is:
\[
[-5, 3]
\]

Would you like a more detailed breakdown, or do you have any other questions? Here are a few related questions to expand your understanding:

1. What is the range of \( f + g \) on the interval \( [-5, 3] \)?
2. How would you graph \( f + g \) by adding the values of \( f(x) \) and \( g(x) \)?
3. What happens to the domain if we consider \( f(x) \times g(x) \) instead of \( f(x) + g(x) \)?
4. How do discontinuities in \( f(x) \) and \( g(x) \) affect the domain of \( f + g \)?
5. What is the relationship between the domain of the sum of two functions and their individual domains?

**Tip:** Always remember, when combining functions, their common domain is determined by where both functions are defined.

Use the graphs of f and g to find the domain of f + g.

Learn how to find the domain of the sum of two functions by analyzing the graphs of f(x) and g(x). This example involves understanding where both functions are defined and finding the overlapping interval. Suitable for high school students in Grades 9-12.

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