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.