Exponential function is one of the important basic elementary functions. Generally y=ax (a is a constant, take a >；; 0, a≠ 1) is called exponential function, and the definition domain of the function is r. In the definition expression of exponential function, the coefficient before ax must be the number 1, and the independent variable x must be in the position of exponent, and it cannot be any other expression of x, otherwise it is not an exponential function.
The extended data exponential function applied to the value e is written as exp(x). It can also be written as ex, where e is a mathematical constant and the base of natural logarithm, which is about equal to 2.7 1828 1828, also known as Euler number.
When a> is in 1, the negative value of exponential function to x is very flat, and the positive value to x rises rapidly. When x equals 0, y equals 1. When 0
As a function of the real variable x. The image of is always positive (above the X axis) and increasing (from left to right). It never touches the X axis, although it can be infinitely close to the X axis (therefore, the X axis is the horizontal asymptote of this image. Its inverse function is natural logarithm ln(x), which is defined on all positive numbers X.
Sometimes, especially in science, what is the more common form of the term exponential function? (k belongs to r), where a is called "base" and is any positive real number that is not equal to 1. This paper initially focuses on the exponential function with Euler number e as the base [3]? .
What is the general form of exponential function? (a>0 and ≠ 1) (x∈R). From the above discussion about power function, we can know that if X can take a whole set of real numbers as the domain, then we only need to make A >: 0, a≠ 1.