UNIT ONE: INTRODUCTION TO FUNCTIONS
LESSON ONE: RELATIONS & FUNCTIONS
Relation: Any set of ordered pairs.
Domain: The set of all x-coordinates in a relation.
Range: The set of all y-coordinates in a relation.
Function:
A relation in which no x-values are repeated.
For every x-value, there is ONE and ONLY ONE y-value.
Vertical Line Test: If a vertical line can be drawn such that it passes through more than one point on a
graph of a relation, then the relation is NOT a function. Otherwise, it is a function.
There are several ways we can represent functions/relations
1.
2.
y  mx  b
f x  mx  b (Function Notation)
3. Mapping Diagrams:
1
5
9
12
-2
0
4
8
Examples:
1. Use the VERTICAL LINE TEST to determine which of the following are functions.
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2. State whether or not the following are functions. State the domain and range.
a) 1,3, 2,1, 3,0, 4,2
b) y  2 x  5
c) y  2 x  1  3
d)
e) y 
f) x 2  2 y 2  36
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x3
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