2.1 Functions

Objectives: Does a relation represent a function? From a set of ordered pairs, equations and graphs (2.2) Evaluating functions Operations with functions

A set of ordered pairs X – domain elements Y – range elements Relation: A set of ordered pairs X – domain elements Y – range elements

Function: A relation in which each domain element is paired with exactly one range element

Is this relation a function? { 1,4 , 2,5 , 3,6 , 4,7 } 1,4 , 2,4 , 3,5 , 6, 10 −3,9 , −2,4 , 0,0 , 1,1 , 3,8 𝑦=2𝑥−5 𝑥 2 + 𝑦 2 =100

Evaluate each function: 𝑓 𝑥 =2 𝑥 2 −3𝑥 𝑓 3 𝑓 𝑥 +𝑓 3 3𝑓 𝑥 𝑓(−𝑥) −𝑓 𝑥 𝑓 3𝑥 𝑓(𝑥+3)

Operations with functions 𝑓+𝑔 𝑥 =𝑓 𝑥 +𝑔 𝑥 𝑓−𝑔 𝑥 =𝑓 𝑥 −𝑔 𝑥 𝑓∙𝑔 𝑥 =𝑓 𝑥 ∙𝑔 𝑥 𝑓 𝑔 𝑥 = 𝑓(𝑥) 𝑔(𝑥) 𝑔 𝑥 ≠0 Do on board: Given f(x) = x^2 + 9 g(x) = 3x + 5 (f+g)(x) (f-g)(x) (f*g)(x) (f/g)(x)

Homework: Pg. 69 #19 – 45 odd #63– 71 odd

2.1 Functions Day 2

Objectives: Find the domain of a function Evaluating a difference quotient

Domain: The largest set of real numbers for which the value 𝑓(𝑥) is a real number

Find the domain of the following functions: 𝑓 𝑥 = 𝑥 2 +5𝑥 𝑔 𝑥 = 3𝑥 𝑥 2 −4 ℎ 𝑡 = 4−3𝑡 𝐹 𝑥 = 3𝑥+12 𝑥−5

Evaluate the function for the difference quotient. Simplify. 𝑓 𝑥+ℎ −𝑓(𝑥) ℎ (ℎ≠0) 𝑓 𝑥 =2𝑥 −5 𝑓 𝑥 =2 𝑥 2 −3𝑥

Homework: Pg. 69 #47 – 61 odd #75, #77