Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

After completing this lesson, you should be able to:After completing this lesson, you should be able to: Determine if a mathematical relation represented Determine if a mathematical relation represented

by a schematic map, a table of values, or a set of by a schematic map, a table of values, or a set of ordered pairs is or is not a function.ordered pairs is or is not a function.

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

Def: A Def: A functionfunction is a mathematical relation between a is a mathematical relation between a collection of input values (the collection of input values (the domaindomain) and a ) and a collection of output values (the collection of output values (the rangerange) in which no ) in which no value in the domain corresponds to more than one value in the domain corresponds to more than one value in the range.value in the range.

A function is usually expressed as an equation that A function is usually expressed as an equation that has been “solved for y” (EX: y = xhas been “solved for y” (EX: y = x2 2 – 3x)– 3x)

A function can also be represented by a schematic A function can also be represented by a schematic drawing, a table of values, or a set of ordered pairsdrawing, a table of values, or a set of ordered pairs

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

Here is an example of a function represented by a Here is an example of a function represented by a schematic drawingschematic drawing

Graphic courtesy of Creative CommonsGraphic courtesy of Creative Commons™™. Created by David Eger, Interactive Mathematics Online (IMO), . Created by David Eger, Interactive Mathematics Online (IMO), ©1994-2009, Drexel University. All rights reserved.©1994-2009, Drexel University. All rights reserved.

RRetrieved from http://library.thinkquest.org/2647/algebra/funcbase.htmetrieved from http://library.thinkquest.org/2647/algebra/funcbase.htm

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

Here is an example of a function represented by a table Here is an example of a function represented by a table of values:of values:

Note that each x-value corresponds to one and only one Note that each x-value corresponds to one and only one y-value.y-value.

0-2-20410y

3210-1-2x

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

The table of values below does not represent a The table of values below does not represent a function. Do you know why?function. Do you know why?

x -3 -2 -1 -1 0 0 1 2

y 9 4 1 0 2 3 4 5

Below are two mathematical relations represented as Below are two mathematical relations represented as sets of ordered pairs. Can you tell which set sets of ordered pairs. Can you tell which set represents a function and which does not?represents a function and which does not?

F = { (4, -2), (1, -1), (0, 0), (1, 1), (4, 2) }F = { (4, -2), (1, -1), (0, 0), (1, 1), (4, 2) } G = { (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4) }G = { (-2, 4), (-1, 1), (0, 0), (1, 1), (2, 4) } F is not a function because it contains at least one x-F is not a function because it contains at least one x-

coordinate which is associated with two different y-coordinate which is associated with two different y-coordinates.coordinates.

G is a function. Each of its x-coordinates is G is a function. Each of its x-coordinates is associated with one and only one y-coordinate.associated with one and only one y-coordinate.

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

Lesson 14Lesson 14Introduction to FunctionsIntroduction to Functions

(Sect. 1.4)(Sect. 1.4)

Remember…whether it is represented by a schematic Remember…whether it is represented by a schematic drawing, a table of values, or a set of ordered pairs, a drawing, a table of values, or a set of ordered pairs, a mathematical relation is a function only if no element mathematical relation is a function only if no element of the domain is associated with more than one of the domain is associated with more than one element of the range.element of the range.

In a future lesson, we will discover how to determine In a future lesson, we will discover how to determine if an equation or a graph represents a function.if an equation or a graph represents a function.