## 15.5 Outline

- Definitions
- first/second components
- function

- Representations of functions
- ordered pairs
- mapping
- machine

- Functional notation
- domain
- range
- difference quotient

- Vertical line test
- Some important functions (see below)
- constant function
- linear function
- quadratic function
- trigonometric function
- exponential function
- logarithmic function
- probability function

## 15.5 Essential Ideas

A **function **is a set of ordered pairs in which the first component is associated with exactly one second component. Use the vertical line test to see if a given graph is a function.

Here are some important functions:

**constant **function:

*f *(*x *) = *k
*

**linear **function:

*f *(*x *) = *mx + b *(*m *is not zero)

**quadratic **function:

*f *(*x* ) = *ax*^{2}* + bx + c* (*a *is not zero)

**exponential **function:

*f *(*x *) = *b ^{x}* (

*b*> 0,

*b*is not one)

**logarithmic **function:

*f *(*x *) = log * _{b}x *(

*b*> 0,

*b*is not zero,

*x*> 0)

**probability **function: A function *P *which satisfies the following properties:

0 ≤ *P *(*E* ) ≤ 1 *P *(*S *) = 1 *S *is the sample space)

*P *(*E *or *F *) =*P *(*E *) +*P *(*F *) (*E *and *F *are mutually exclusive)