Draw a graph and label important points of this function g is decreasing on the interval (−7, 6). It is also known that g(x) is even everywhere

Here is the graph of the function \( g(x) \) with the important points labeled:

- **\( g(-7) \)** and **\( g(7) \)**: These points are symmetric because \( g(x) \) is even.
- **\( g(0) \)**: This is the minimum point of the function because \( g(x) \) decreases from both sides towards \( x = 0 \).

If you have any further questions or need additional explanations, feel free to ask!

### Follow-up Questions:
1. What would happen to the graph if the interval where \( g(x) \) is decreasing changed?
2. How does the symmetry of the function help in graphing it?
3. How would the graph look if \( g(x) \) were odd instead of even?
4. What can you say about the behavior of \( g(x) \) outside the interval \([-7, 7]\)?
5. How does labeling important points aid in understanding the function's behavior?

### Tip:
Labeling key points on a graph helps in visualizing and understanding the behavior of the function more effectively, especially when considering properties like symmetry and intervals of increase/decrease.

Explore how to graph a function g(x) that is decreasing on the interval (-7, 6) and is even everywhere. Learn about the symmetry properties and important points such as maximum, minimum, and symmetric points. Suitable for high school students studying functions and symmetry in mathematics.

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