Summary 1 Relations Domain Range and Rule Domain

Summary 1

Relations: Domain, Range, and Rule Domain is the set of all permissible values of the independent variable Range is the set of all permissible values of the dependent variable. Permissible values of a variable Ø will not make the denominator zero Ø will not make the radicand of even index negative

Functions 3

Functions Definition Function A function f from A to B is a relation from A to B where to each , there corresponds exactly one such that A function can also be defined as a set of ordered pairs in which no two ordered pairs have the same first component but different second components. 4

SOME EXAMPLES OF FUNCTIONS n Functions as set of ordered pairs f = {(1, 1), (3, 5), (4, 6), (8, 9)} g = {(1, 0), (2, 0), (-1, 5)} n Functions as graphs n Functions as equations f(x) = x 2 + 1 g(x) = 4 - 5 x n Functions as table of values No. of eggs (x)x Price of breakfast (y) 1 P 10. 00 2 P 18. 00 3 P 22. 00 5

Functions For each relation, determine if it is a function. Yes r 1= {(1, 3), (2, 5), (3, 8), (4, 10)} r 2 = {(-1, 0), (2, -3), (. 5, 1), ( 2/3, 1/2)} Yes r 3 = {(x, y)| y= 2 x-5} Yes r 4 = {(x, y)| y= x 2} Yes r 5 = {(x, y)| y > x-3} No No 6

Vertical Line Test for a Function (a) y 3 – x = 1 (b) y 2 – x 2 = 9 7

Vertical Line Test for a Function Which of the following graphs represent a function? x y Yes x x y No x y Yes 8

Which of the following mapping diagrams represent functions? Yes No 9

TIME TO THINK 1. The following data were collected from members of a college pre-calculus class. Is the set of ordered pairs (x, y) a function? a) x Height y Weight 72 in. 180 lb 60 in. 204 lb 60 in. 120 lb 63 in. 145 lb 70 in. 184 lb 10

TIME TO THINK 2. The following data were collected from members of a college pre-calculus class. Is the set of ordered pairs (x, y) a function? b) x year of graduation y number of graduates 2005 2 2006 12 2007 18 2008 7 2009 1 11

Function Notation Suppose you’re given the equation § § f(x) should be read “f of x “, NOT “f times x”. f is the name of the function; it’s not a number. x is the input value or independent variable. f(x) is the value of the function f at the number x. 12

Function Notation Suppose you’re given the equation §We may replace f(x) by y. That is, f(x) = y which means that the value of the function is the y value. What does mean? The value of f when x = 2 is 10. 13

Interpretation of f(x) 14

Evaluating a function 15

Evaluating a function Evaluate the following functions at x = 1. 5 16

Evaluating a function Evaluate the following functions at x = 1. 5 17

Evaluating a function n 18

TIME TO THINK n 19

TIME TO THINK n 20