Notes Booklet

Functions 10

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Relations and Sets

set a of distinct objects

element any in a set

relation the elements of set with the elements of set

Set Notation (Ordered Pairs)

{ (Hull, Chicago), (Orr, Boston), (Howe, Detroit), (Esposito, Boston), (Horton, Toronto), (Beliveau, Montreal) }

{ (472, 239), (–100, –47), (4, 5), (–38, –16) }

Mapping Notation Table of Values

Equation Cartesian Plane Graph

y = 12.75x + 50

Statement

one–half a number less ten

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Domain and Range

domain : the values of the ( ) variable

range : the values of the ( ) variable

Expressing Domain and Range 1

{ } are used to show the set

points must be expressed

elements are listed , in order from

D : D :

R : R :

Expressing Domain and Range 2

a relationship can be expressed with :

(1) notation < > ≤ ≥

(2) notation [includes], (does not include)

D :

R :

Functions

a relation is a if there is (y) value for each (x) value

Vertical Line Test For Functions

a graph represents a when on the graph lie on

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Function Notation

C(n) = 27.50n + 500

function notation: shows the variable in a function

the function relates the cost (dependent) to the number of people (independent)

read as : “the Cost of (n) people is 27.50 each plus 500”

any function that can be written as an equation in can also be written in notation

y = 3x – 1 becomes y(x) = 3x – 1

said as : “the y of (x) is 3x – 1”

put the independent variable in

the (function) stays the

V = – 34 t + 6

N = 0.6t + 24

C(n) = 8n – 1250

y(x) = 34x + 5

Using Function Notation to Determine Values

C(n) = 17.50n + 250(the Cost of (n) people is 17.50 per person plus 250)

1. to solve for a specific “n” value ex. C(80)

the into the equation and solve

i.e. the Cost of 80 people C(80) = 17.50(n) + 250= 17.50(80) + 250= 1650

2. to solve for a function value ex. C(n) = $1037.50

solve for by

solve: C(n) $1037.50 1037.50 = 17.50(n) + 250–250.00 –250.00 787.50 = 17.50(n) 787.50 = 17.50(n)

17.50 17.50

45 = n

Properties of Linear Relations

y(x) = mx + b

linear relation a function that forms a on a graph

the is always read from

the of can be found by calculating:

change∈dependent variablechange∈independent variable = rise

run = ∆ y∆x

Horizontal Intercept

the – intercept (i.e., when )

the ( , 0) where the graph crosses the

Vertical Intercept

the – intercept (i.e., when )

the ( 0, ) where the graph crosses the

Identifying Linear Functions

y(x) = mx + b (where m = Δ yΔ x = ❑❑)

Identifying Linear Equations From Word Statements

y(x) = mx + bQuestion : Which value depends on the other?

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