2. 2.1 Relations and Functions
Objective – To be able to represent relations and functions.
– To be able to graph and evaluate linear functions.
Relation – Is a set of pairs of input and output values.
Ordered Pair – A representation of a Relation, in the form of (x,y).
Domain – Is the set of all inputs (x coordinate).
Range – Is the set of all outputs (y coordinate).
Function – Is only a relation when there is ONLY one output for each input ***N0 duplicate X-values***

3. o Coordinate Plane: Quadrant II Quadrant I Quadrant III Quadrant IV
Y-axis o
Quadrant II
Quadrant I
X-axis
-9 –8 –7 –6 –5 –4 –3 –2
Origin
(0,0)
Quadrant III
Quadrant IV

4. Example 1 & 2 Graph the Relations: (-3,-1), (-1, 1), (1,1), (2,3)
Then find the Domain and Range: –5 –4 –3 –2 –1 1 2 5 4 3
Domain: -3,-1,1,2
(2,3)
Range:-1,1,3
(-1,1)
(1,1)
(-3,-1)

5. Vertical Line Test For Functions
A relation is a function if and only if no vertical line intersects the graph at more than one point.
Example 3
Determine if the graph in example 2 is a function. –5 –4 –3 –2 –1 1 2 5 4 3
Yes this is a Function.

6. Example 4 Determine if the graph is a function.–5 –4 –3 –2 –1 1 2 5 4 3
This is NOT A Function.

7. Making a mapping diagram
Example 5: Make a mapping diagram for the relation {(-1,-2), (3,6), (-5,-10), (3,2)}
Domain Range
-10 -2 2 6 -5 -1 3

8. The equation y = x + 4 is a linear function because there are no exponents.
By naming a function “f” you can write the function using function notation f(x) = x + 4.
Example 5
Decide whether the function is linear. Evaluate the function when x = 3
a) f(x) = x2 + 4x - 1
b) g(x) = -3x + 4
f(x) is not a linear function because it has an x2 term.
g(x) is a linear function.
g(3) = -3(3) + 4
f(3) = (3)2 + 4(3) - 1
g(3) = = -5
f(3) = – 1 = 20

9. Guided Practice
Due Today:
All-In-One Workbook
Practice 2-1 (4-17) all

10. HOMEWORK Due Next Class: Pg. 61 – 63
(1-25 )eoo (33-39 ,43-45) odd, 50, 51