Functions are nice machines! You put something in, and it produces something predictable.
Definition
A function consists of:
1. a set of inputs, called the domain.
2. a rule which assigns each input to exactly one output.
3. a set of outputs, called the range.
Function Notation
How do we write functions? Using function notation! Function notation is written as follows:
Videos
Watch this video for some examples demonstrating function notation and function evaluation.
Watch this video for function notation and evaluation using graphs and tables.
Definition
A function is one-to-one if implies that
. This means that every output must have a unique input.
To determine if a graph corresponds to a one-to-one function, we need to check two things:
- its a function
- its one-to-one
This is important when we get to section 3.7 on Inverses.