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
{(6, 5), (2, 3), (1, 4), (0, 3)} 𝑥
6
Table 𝑦
5
Graph Mapping
2
1
0
3
4
3
Ways to see if a Relation is a Function
Domain: any repeated values? Functions will never have repeated values in the domain.
Ordered Pairs
Any repeated xvalues? Functions will ____________ have repeated xvalues.
Table
Look for repeated x-value coordinates.
Functions will never have repeated
_______________.
Graph
Vertical Line/Pencil
Test – draw vertical lines through the graph. Vertical lines will never hit the function more than once.
Mapping
Are there more than one arrow coming from one number on the left?
Functions never have multiple arrows leaving from any element in the
_____________.

Example 1:
9
0
6
8
12
21
0
6
1
Is this mapping a function?
Why?
Mapping
Example 2:
-1
0
2
3
-2
4
0
6
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:
Domain:
Range:
Example 2:
Domain:
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.

Another way of saying _________

Does NOT mean 𝑓 ∙ 𝑥
 Read as “ 𝑓 of 𝑥 ”
The function or rule 𝑓(𝑥) = 3𝑥 + 2
Name of the function Tells what number to plug into the ___________
Old Way
What is 𝑦 = 3𝑥 + 2 , when 𝑥 = 5 ?
Function Notation 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 the function rule: 𝑓(𝑥) =
12 𝑥 𝑥 𝑦
−4
−1
3
6
6. Complete the following table using the function rule: 𝑓(𝑥) = 𝑥 2 − 6 𝑥 𝑦
−2
−1
0
1