Through (0, 1), through the second and first quadrants, the domain is r, and the range is f (x) >; 0, f(x) increases with the increase of x in the definition domain.

When x->; F(x)=0 when-∞

When x->; F(x)=+∞ When +∞

Exponential function is an important function in mathematics. This 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.

Extended data

As a function of the real variable x, the image of y=ex 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.

The important point of exponential function based on E is that its function is equal to its derivative. E is irrational number and transcendental number (see Lindemann-Weierstrass theorem). This is the first proved transcendental number, which is not deliberately constructed (compare Liouville number); Proved by Charles Hermite in 1873.

References:

Baidu encyclopedia-exponential function