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.

Example of a Function

Example of a Non-Function

y = x + 3

y = ± x

Important Definitions

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.

Further Discussion

  • What do functions look like?
  • What do non-functions look like?