The function e^-x^2 is a mathematical expression where e is the base of the natural logarithm, approximately equal to 2.718. The exponent -x^2 indicates that as x increases or decreases, the value of the function decreases rapidly towards zero. This function is often used in probability and statistics, particularly in the context of the normal distribution. The graph of e^-x^2 is bell-shaped and symmetric around the y-axis. It reaches its maximum value of 1 when x = 0 and approaches zero as x moves away from zero in either direction. This behavior makes it useful in various fields, including physics and engineering, for modeling phenomena that exhibit rapid decay.