# Functions

### Notes

**A function is a special relationship between values: Each of its input values gives back exactly one output value.**

** It is often written as "f(x)" where x is the value you give it.**

**IMPORTANT TERMS:**

**Input-Domain-Independent-x****Output-Range-Dependent- y- f(x)**

** DETERMINING IF A RELATION IS A FUNCTION:**

**Mapping/Tables: check input/output rule****Vertical Line Test: Draw a vertical line through the graph. If the vertical line touches more than one point on the graph, it is not a function. This means that the x value along the vertical line has more than ONE output.**

**REMEMBER:**

There are different ways to represent the same information. An input/output table is a way to organize your work and ordered pairs. The ordered pairs translate to the graph forming a pictorial representation of the function. The algebraic equation provides a rule that can be used to determine the output for any given input.