Function Notation
What is Function Notation?
Function notation is an efficient way to describe relationships between quantities that vary in a functional relationship.
Function
The function showed here is called a linear function. The domain of a linear function is (-∞,∞) and the range is (-∞.∞). The domain and range is as such because you can input any value between -∞ and ∞ and get anything in the range of -∞ and ∞. This is a function because you can input a value and get a an output based on the formula that is used to get your outputs.
But Is this a Function?
In this graph you see a circle. Notice the circle touches the points (3,0), (0,3), (-3,0), and (0,-3). This means the output will never extend beyond these points. So your domain for this graph is (-3,3) and the range is (-3,3). This is not a function though because when you perform the vertical line test you touch more than 1 point when moving across the circle.
Recursive Formulas
Each of the above scenarios can be represented in recursive formulas.
- The linear scenario can be represented as tn=tn-1+3
- The exponential function can be represented as tn=tn-1*2