This lesson introduces the concept of functions, defining them as mathematical relations between input values (domain) and output values (range) where each input corresponds to one output. It discusses various representations of functions, including equations, schematic drawings, tables of values, and sets of ordered pairs, while emphasizing that a relation is a function only if no input is linked to multiple outputs. Examples are provided to illustrate relations that do and do not qualify as functions.

1. Lesson 14 Introduction to Functions (Sect. 1.4) After completing this lesson, you should be able to: Determine if a mathematical relation represented by a schematic map, a table of values, or a set of ordered pairs is or is not a function.

2. Lesson 14 Introduction to Functions (Sect. 1.4) Def: A function is a mathematical relation between a collection of input values (the domain ) and a collection of output values (the range ) in which no value in the domain corresponds to more than one value in the range. A function is usually expressed as an equation that has been “solved for y” (EX: y = x 2 – 3x) A function can also be represented by a schematic drawing, a table of values, or a set of ordered pairs

3. Lesson 14 Introduction to Functions (Sect. 1.4) Here is an example of a function represented by a schematic drawing Graphic courtesy of Creative Commons ™ . Created by David Eger, Interactive Mathematics Online (IMO), ©1994-2009, Drexel University. All rights reserved. R etrieved from http://library.thinkquest.org/2647/algebra/funcbase.htm

4. Lesson 14 Introduction to Functions (Sect. 1.4) Here is an example of a function represented by a table of values: Note that each x-value corresponds to one and only one y-value. 0 -2 -2 0 4 10 y 3 2 1 0 -1 -2 x

5. Lesson 14 Introduction to Functions (Sect. 1.4) The table of values below does not represent a function. Do you know why? x -3 -2 -1 -1 0 0 1 2 y 9 4 1 0 2 3 4 5

6. Below are two mathematical relations represented as sets of ordered pairs. Can you tell which set represents a function and which does not? F = { (4, -2), (1, -1), (0, 0), (1, 1), (4, 2) } G = { (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4) } F is not a function because it contains at least one x-coordinate which is associated with two different y-coordinates. G is a function. Each of its x-coordinates is associated with one and only one y-coordinate. Lesson 14 Introduction to Functions (Sect. 1.4)

7. Lesson 14 Introduction to Functions (Sect. 1.4) Remember…whether it is represented by a schematic drawing, a table of values, or a set of ordered pairs, a mathematical relation is a function only if no element of the domain is associated with more than one element of the range. In a future lesson, we will discover how to determine if an equation or a graph represents a function.