1. 1.4 Relations & Functions

2. 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)

3. 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

4. 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

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)

6. 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

7. #204 Worksheet 1-4 Relations, Functions & Difference Quotient
Homework
#204 Worksheet Relations, Functions & Difference Quotient