ExponentialAbs

ExponentialAbs is a mathematical function that combines the exponential function with the absolute value function. It is defined as e raised to the power of the absolute value of x, or symbolically, ExponentialAbs(x) = e^|x|. The absolute value function, |x|, returns the non-negative value of x, meaning it is x if x is zero or positive, and -x if x is negative. The exponential function, e^x, is a fundamental mathematical constant. When these two are combined, the resulting function always produces a non-negative output.

The domain of ExponentialAbs(x) is all real numbers. The range of ExponentialAbs(x) is all real numbers greater than or equal to 1. This is because the smallest possible value for |x| is 0 (when x=0), and e^0 equals 1. For any other real number x, |x| will be a positive value, and e raised to a positive power will always be greater than 1.

The graph of ExponentialAbs(x) is symmetric about the y-axis, a characteristic inherited from the absolute value function. For positive values of x, the graph is identical to the standard exponential function e^x. For negative values of x, the graph is a reflection of the positive side across the y-axis, mirroring the behavior of e^(-x). This function has applications in various fields, including physics and engineering, particularly in modeling phenomena where growth or decay is influenced by magnitude rather than sign.