The basics of functions depends on two quantities, one which is given, the input, and one that is produced, the output. A function associates a single output to each input element drawn from a fixed set. For example if and 'x' value in an equation produces two possible 'y' values, then the equation is not a function.

Function notation - Function notation is a symbolic representation of a function with a variable. This can be expressed as f(x). This is read: f of x, not f times x. where f is the function or output and x is the variable or input. An example of this notation would be this expression defining a function, f(x)= x + 2. If we take the input or variable and assign it the value 2, f(x) becomes x + 2 or f(2) = (2) + 2 or f(2) = 4.

Continuous Functions - In a continuous function a small change in the input(x) will result in a small change of the output(f). For example all Polynomial functions are continuous. A polynomial is an expression that is made up of variables, constants and the operations of multiplication, subtraction, addition, and positive exponents. An example of a polynomial function and a continuous function is f(x)=x²+3x-4. Another kind of a continuous function is a exponential functions. On a graph their will be no holes or missing spaces between two points. The When you draw the graph of a continuous function you never have to lift your pencil from the paper. Each point touches the next point.
Discontinuous Function/Discrete function - A discontinuous function and a discrete function are almost the same thing. A discontinuous function is a function that is not continuous. Some points connect to make the line continues. A discrete functions is a discontinuous function madde up of all separate or discrete points that will not necessarily connect.

FunctionsThe basics of functions depends on two quantities, one which is given, the

input, and one that is produced, theoutput. A function associates a single output to each input element drawn from a fixed set. For example if and 'x' value in an equation produces two possible 'y' values, then the equation is not a function.## Table of Contents

Example of a Function

Example of a Non-Function

Important DefinitionsFunction notation- Function notation is a symbolic representation of a function with a variable. This can be expressed as f(x). This is read: f of x, not f times x. where f is the function or output and x is the variable or input. An example of this notation would be this expression defining a function, f(x)= x + 2. If we take the input or variable and assign it the value 2, f(x) becomes x + 2 or f(2) = (2) + 2 or f(2) = 4.Continuous Functions- In a continuous function a small change in the input(x) will result in a small change of the output(f). For example all Polynomial functions are continuous. A polynomial is an expression that is made up of variables, constants and the operations of multiplication, subtraction, addition, and positive exponents. An example of a polynomial function and a continuous function is f(x)=x²+3x-4. Another kind of a continuous function is a exponential functions. On a graph their will be no holes or missing spaces between two points. The When you draw the graph of a continuous function you never have to lift your pencil from the paper. Each point touches the next point.- A discontinuous function and a discrete function are almost the same thing. A discontinuous function is a function that is not continuous. Some points connect to make the line continues. A discrete functions is a discontinuous function madde up of all separate or discrete points that will not necessarily connect.Discontinuous Function/Discrete function

Further Discussion