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) = 2x2 + 7 *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

Remember – No dividing by 0 – No taking even roots of neg. #s If a function has no domain specified, it is “All Real #s” (R) You have to find domain? Ex 1) Find Domain & Range (confirm with graph) a) b) Remember – No dividing by 0 – No taking even roots of neg. #s Graph on Calculator so…x ≠ 0 Graph on Calculator so…x < 5

Determining if a relation / rule / mapping is a function… Vertical Line Test!! all vertical lines drawn only touch graph 1 time – then YES! Ex 2) Are these functions? a) one-to-one function? passes horizontal line test b) c) y = 5 N/A (not a function) YES! NO! YES! NO! (basically, no y’s repeat)

Difference Quotient Ex 3) Given f (x) = x2 + 1, find: f (1) = (1)2 + 1 f (–5) = (–5)2 + 1 f () = ()2 + 1 f (+ ) = (+ )2 + 1 f (x + h) = (x + h)2 + 1

#204 Worksheet 1-4 Relations, Functions & Difference Quotient Homework #204 Worksheet 1-4 Relations, Functions & Difference Quotient