Chapter 2 & 7 VOCAB & NOTES

Relation & Functions (2-1, 7-7, 7-8)

relation

relation

a set of ordered pairs

List: {(2, 3), (3, 4), (4,5)}

Graph: plotting points

Mapping: domain and range sets *numerical order, least → greatest, do not repeat members in a set, arrows indicating which y goes with each x

Table: list each x and y in relation

Sentence: y=2x-8

domain

the set of x-values (or first members) of every ordered pair; the input; the independent variable

range

the set of y-values (or second members) of every ordered pair; the output; the dependent variable

function

special type of relation; a relation in which every member of the domain maps to exactly one member of the range. In order to be a function, a member of the domain, cannot be repeated.

function notation

f(x)=ax+b f(x) is the name of the function; ax+b is how the function is defined

composition functions

start inside → out

discrete functions

disconnected e.g. {(3, 4), (4, 5), (5,6)}

continuous functions

connected e.g. y=x+1

REVIEW

identify

Domain: given graph → [0, ∞); given list → {-6, 5, 10}

Range: (-∞, ∞) → {1}

Relation or Function?

Continuous or Discrete?

composition

exists if the range of g(x) is a subset of the domain of f(x)

inverse function

a function has an inverse if it satisfies the horizontal pencil test

f(a)=b if and only if f^-1(b)=a

REVIEW for 2-1, 7-7, 7-8

Evaluate a function

Graph a relation

Find values of functions

Find inverse and composition of functions

VOCAB: domain, range, vertical line test

Discrete vs. continuous, domain vs. range, function vs. relation

Composing ordered pairs