AFDA – Unit 1: Linear Functions Pt 1
Day 4 Notes: Relations, Functions, D/R
Name: _________________
Block: _____ Date:_______
Relation – any set of __________________________________________________.
 A function is a relation in which no set of _____________ values repeat.
Domain – the _______________________, _________________, or ______ values.
 List in order from smallest to biggest
Range – the _______________________, _________________, or ______ values.
Ways to Express Relations
Domain: {0, 1, 2, 6}
Range: {3, 3, 4, 5}
Ordered Pairs
Table
{(6, 5), (2, 3), (1, 4), (0, 3)}
Graph
𝑥
6
𝑦
5
2
3
1
4
0
3
Mapping
Ways to see if a Relation is a Function
Domain: any repeated values? Functions will never have repeated values in the
domain.
Ordered Pairs
Table
Graph
Mapping
Any repeated xvalues? Functions
will ____________
have repeated xvalues.
Look for repeated
x-value
coordinates.
Functions will never
have repeated
_______________.
Vertical Line/Pencil
Test – draw vertical
lines through the
graph. Vertical lines
will never hit the
function more than
once.
Are there more
than one arrow
coming from one
number on the left?
Functions never
have multiple
arrows leaving from
any element in the
_____________.
Mapping
Example 1:
Example 2:
9
12
0
21
6
0
8
6
-1
-2
0
4
2
0
3
6
1
Is this mapping a function?
Why?
Is this mapping a function?
Why?
Graphs (Ordered Pairs/Coordinate Points)
Use the mappings above to make ordered pairs/co-ordinate points, then plot example
2.
Example 1:
Example 2:
Domain and Range
Use the mapping diagrams and ordered pairs/coordinate points to help write your
domain and range for each example.
Example 1:
Example 2:
Domain:
Domain:
Range:
Range:
A function can be thought of as a machine that assigns _______ _________ to
________ ___________.
Input
X-Value
Domain
Independent Variable
Function Rule
(in function notation)
𝑓(𝑥) =
Output
Y-Value
Range
Dependent Variable
Function Notation
If something is written in function notation we know that the relation described by the
equation must be a function.
The function or rule
{
Another way of saying _________
Does NOT mean 𝑓 ∙ 𝑥
Read as “𝑓 of 𝑥”
{



𝑓(𝑥 ) = 3𝑥 + 2
Name of the function
Tells what number to plug
into the ___________
Old Way
Function Notation
What is 𝑦 = 3𝑥 + 2, when 𝑥 = 5?
𝑓(𝑥) = 3𝑥 + 2, find 𝑓(5).
or
𝑓(5) = 3𝑥 + 2
Mixed Function Notation Practice.
Evaluate the following using 𝑓(𝑥) = 3𝑥 + 2.
1. 𝑓(3)
2. 𝑓(−2)
3. What is the range of the function 𝑓(𝑥) = 5𝑥 2 + 9 when the domain is {−3, 0, 1}?
4. What is the range of the function 𝑓(𝑥) = 5 − 8𝑥 when the domain is {−2, 2, 4}?
5. Complete the following table using
12
the function rule: 𝑓(𝑥) =
6. Complete the following table using
the function rule: 𝑓(𝑥) = 𝑥 2 − 6
𝑥
𝑥
𝑦
𝑥
−4
−2
−1
−1
3
0
6
1
𝑦