https://file.aiquickdraw.com/mathbot/file/1725504515180mkaip5p1.jpg

Here is the graph of the function \( y = e^{x^2} \). As you can observe:

- The function grows rapidly as \( x \) moves away from zero.
- It is symmetric around the y-axis due to its even nature.
- At \( x = 0 \), the value is \( y = 1 \), and the slope of the curve is flat.
- The function shows an exponential increase both in the positive and negative directions for large values of \( |x| \).

Would you like further details on any specific aspect of the function or its behavior?

Here are some related questions for deeper exploration:
1. How does the derivative of \( y = e^{x^2} \) behave as \( x \) increases?
2. What are the implications of the second derivative for concavity?
3. How does the function compare to other exponential functions, like \( e^x \)?
4. What happens to the function's value as \( x \to \infty \)?
5. Can this function be approximated for small \( x \) values?

**Tip**: Symmetry in functions can greatly simplify graph analysis, especially when studying even or odd functions.

y = e^{x^2} fonksiyonunun değişimini inceleyip, grafiğini çiziniz.

Explore the graph and behavior of the function y = e^{x^2}, focusing on exponential growth, symmetry around the y-axis, and changes in slope. This analysis is suitable for high school students studying advanced mathematics.

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