MTH 070 Elementary Algebra Section 3.6 Introduction to Functions Chapter 3 Linear Equations, Slope, Inequalities, and Introduction to Functions Copyright © 2010 by Ron Wallace, all rights reserved.

Relation A rule in which the value of one quantity/variable determines the value of a second quantity/variable. Examples: Parent in this class  name of child Item in a store  price Car in a parking lot  license plate # Shelve in a library  book Radius of a circle  Area of the circle

Domain The set of all possible values for the first quantity/variable of a relation. Examples: Parent in this class  name of child Item in a store  price Car in a parking lot  license plate # Shelve in a library  book Radius of a circle  Area of the circle

Range The set of all determined values of the second quantity/variable of a relation. Examples: Parent in this class  name of child Item in a store  price Car in a parking lot  license plate # Shelve in a library  book Radius of a circle  Area of the circle

Function A relation in which each value of the domain determines exactly one value in the range. Examples: Parent in this class  name of child Item in a store  price Car in a parking lot  license plate # Shelve in a library  book Radius of a circle  Area of the circle

Numerical Functions (i.e. domain & range are sets of numbers) A relation in which each value of the domain determines exactly one value in the range. Examples: Integer  square Non-Negative integer  square root Real number  one more than double

Numerical Functions (i.e. domain & range are sets of numbers) Set of ordered pairs each with a different first number. Examples: Integer  square Non-Negative integer  square root Real number  one more than double { (1,1), (2,4), (-3,9), … } { (1,1), (4,2), (9,3), … } { (0,1), (5,11), (-2,-3), … } { (1,7), (2,4), (3,7) } NOTE: In most cases, you will not be able to list all of the ordered pairs!

Given a graph … does it represent a function? Vertical Line Test If all possible vertical lines each intersect the graph at no more than one point, the graph is a function.

Function Notation Function Machine Each input produces a single output. Example: { (1,7), (3,-2), (9,0), (-2,7) } Inputs (i.e. domain): 1, 3, 9, -2 Outputs (i.e. range): 7, -2, 0 Notation: (note: a function can be given any name) f(1) = 7f(3) = -2 f(9) = 0f(-2) = 7 Not: “f times 1 is 7” Read as: “f of 1 is 7”

Functions Given as Expressions Example … f(x) = 2x – 3 f(1) = f(0) = f(-3) = f(a) = f(a+5) = f(a) + 5 = f(2x – 1) = 2f(x) – 1 =

Graphing Functions Given as Expressions f(x) = 2x – 3 Equivalent to graphing: y = 2x – 3