What are the basic elementary functions?

There are constant functions, power functions, exponential functions, logarithmic functions, trigonometric functions and anti-trigonometric functions.

Basic elementary functions include the following:

(1) constant function y=c(c is a constant)

(2) power function y = x a (a is a constant)

(3) exponential function y = a x(a >；; 0，a≠ 1)

(4) logarithmic function y = log (a) x (a >; 0, a≠ 1, real number x>0)

(5) trigonometric functions and inverse trigonometric functions (such as sine function: y=sinx arcsine function: y=arcsinx, etc.). )

Definition of power function: Generally speaking, a function with the shape of y=xα(α is a rational number), that is, a function with the base as the independent variable, the power as the dependent variable and the exponent as the constant is called a power function. For example, functions y=x0, y=x 1, y=x2, y=x- 1 (note: x≠0 when y = x-1/xy = x0) are all power functions. The general form is as follows: (α is a constant, which can be a natural number, a rational number, or any real number or complex number. )

Exponential function definition: 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. The general form is as follows: (a>0, a≠ 1)

Definition of logarithmic function: generally speaking, the function y = logax(a >；; 0, and a≠ 1) is called logarithmic function, that is, a function with power (real number) as independent variable, exponent as dependent variable and base constant as constant is called logarithmic function.

Where x is the independent variable and the domain of the function is (0, +∞), that is, x >；; 0。 It is actually the inverse function of exponential function, which can be expressed as x=ay. Therefore, the stipulation of a in exponential function is also applicable to logarithmic function. The general form is as follows: (a>0, a≠ 1, x>0, especially when α=e, expressed as y=lnx).

There are six common trigonometric functions:

Sine function: y=sinx

Cosine function: y=cosx

Tangent function: y=tanx

Cotangent function: y=cotx

Secant function: y=secx

Cotangent function: y=cscx

In addition, there are trigonometric functions that are rarely used, such as forward vector and complementary vector.

There are six kinds of inverse trigonometric functions:

Arcsine function: y=arcsinx

Inverse cosine function: y=arccosx

Arctangent function: y=arctanx