1.4 Relations & Functions

Relation: a set of ordered pairs Domain (D): set of first coordinates of the pairs Range (R): set of second coordinates of the pairs Correspondence between domain & range is mapping Special mapping is a function! (usually x-value) (usually y-value)

Function: f ; a relation in which each element in the domain is mapped to exactly one element in the range  can we put this in our own words??... Relations & functions can be expressed in different ways  one popular one: f (x) such as f (x) = 2x *remember to evaluate f (x) for a particular value of x, simply replace the value for x every time you see an x or g(x) = cos x

Ex 1) Given, evaluate: a) b) c) *this one is something special…but we don’t want to spill the secret quite yet!

If a function has no domain specified, it is “All Real #s” ( R ) You have to find domain? Ex 2) Find Domain & Range (confirm with graph) a) b) Remember – No dividing by 0 – No taking even roots of neg. #s so…x ≠ 0 so…x < 5 Graph on Calculator Graph on Calculator

Two functions are equal if (1)the domain of f is equal to domain of g AND (2)for all x in domain, f (x) = g(x) Ex 3) Are these functions equal? NO…. Domains are same but… h(x) ≠ m(x)

Determining if a relation / rule / mapping is a function… Vertical Line Test!! all vertical lines drawn only touch graph 1 time – then YES! Ex 4) Are these functions? a) one-to-one function? passes horizontal line test y = 5 b) c) (basically, no y’s repeat) YES! NO! N/A (not a function)

Homework #104 Pg 29 #1-23 odd, 24-27, 28, 35, 37, 38, 43, 44, 45, 49, 53, 55, 57