1. Transcendental Functions

A transcendental function is a mathematical function whose graph cannot be drawn on a Cartesian plane (a plane defined by two perpendicular axes). There are many examples of transcendental functions, including the exponential function, sine, cosine, logarithm, and trigonometric functions.

2. Trigonometric Functions

The trigonometric functions are the basic functions of mathematics. These functions are based on angles and their relationships. The three primary trigonometric functions are sine, cosine and tangent. Sine is the ratio between the length of the opposite side of a right triangle and the hypotenuse. Cosine is the ratio between adjacent sides of a right triangle. Tangent is the rate at which the slope of a line changes.

3. Exponential Function

The exponential function is the power series representation of the natural logarithm. The natural logarithm is the inverse of the base 10 logarithm. In other words, the natural logarithms base 10 of any number x is equal to its antilogarithm base e. The exponential function is denoted by the letter E.

4. Logarithmic Functions

Logarithms are a type of exponentiation. A logarithm is a way of representing a number in terms of a different number. The logarithm of a number x is the exponent of the base b. The logarithms base 2 of any number x is called the binary logarithm. Base 8 is known as octal and base 16 is hexadecimal.

5. Algebraic Functions

Algebraic functions are functions that have algebraic forms. An example of an algebraic function is y x^2 + 4x - 5.