Draw a graph 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 \( g(x) \), which is decreasing on the interval \((-7, 6)\) and is even everywhere:

- The function decreases from \( x = -7 \) to \( x = 0 \), and then continues decreasing symmetrically from \( x = 0 \) to \( x = 7 \).
- The graph is symmetric with respect to the y-axis, reflecting the property that \( g(x) = g(-x) \).

Would you like any further details, or do you have any questions?

### Follow-up Questions:
1. How would the graph change if the function were odd instead of even?
2. What would the graph look like if \( g(x) \) were increasing on a different interval?
3. Can you identify the local minimum of the function on this graph?
4. How does the concept of symmetry impact the behavior of functions in general?
5. What are other types of symmetry (besides even and odd) that functions might exhibit?

### Tip:
When sketching graphs, always check for symmetry properties (even, odd) and behavior on key intervals to accurately represent the function.

Explore the graph of the function g(x), which is even and decreasing on the interval (-7, 6). Understand its symmetry properties and behavior across the specified interval. Suitable for high school students studying functions and symmetry in mathematics.

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