Classification,+ Comparison+and+Contrast+Version+2

The Functions can be classified into three branches: Affine functions, Exponential Functions and Trigonometric Functions. · ** Affine Functions: ** These functions are those that changes at constant rate with respect to its independent variable. These can be written with the expression:

y = M x + b ; or y = x^n + x^n-1 +...+ x^n-m + b

Where: "**y**" It is the dependent variable. "**x**" It is the independent variable. "**M**" It is the slope of the function. "**b**" It is a constant that represent a court on Y axis by the line expressed by the function in the Euclidean space.
 * Exponential Functions: ** These functions are of the form:

y = a ^ x

"**a**" It is a constant, that represent the **Base** "**x**" it is the Independent variable and represent the **Exponent** of the function. and has a exponential growing with a constant rate respect to the values assigned to its independent variable. · ** Trigonometric Functions: ** These functions are those that establish a relation between the angles and its oscillatory characteristic, with circumscribed triangles in a circumference, where the independent variable in the function represents the sweep angle.

Some expressions of trigonometric functions are:

y = Sen ( x ) ; y = Cos ( x )

y = Sen (x) / Cos (x) = Tg ( x )

The function has features that difference it of the other operations in calculus. When you assign a value to the independent variable, you will obtain a new value of the depended variable. In other words, it works like a machine, where you put the "material" and in the end of the process, you will obtain a "Product".
 * Comparison and Contrast: **

That is the relevant difference between the functions and other operations in math like the Matrix's, determinants, that doesn't depend of variables.

On the other hand, there are other operations that are functions but uses different operator to obtain some useful values.

For Example: The Integral use functions to calculate the down area of a curve using integral properties to modify the functions.