Download 2.1 Functions and Their Graphs

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***
Coordinate Plane:
Y-axis
Quadrant II
-9 –8 –7 –6 –5 –4 –3 –2
Quadrant I
o
1 2 3 4 5 6 7 8 9
Origin
(0,0)
Quadrant III
Quadrant IV
X-axis
Example 1 & 2
Graph the Relations: (-3,-1), (-1, 1), (1,1), (2,3)
Then find the Domain and Range:
5
Domain: -3,-1,1,2
4
Range:-1,1,3
3
(-1,1)
(2,3)
2
(1,1)
1
–5 –4
–3 –2
(-3,-1)
–1
–1
–2
–3
–4
–5
1
2
3
4
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
Yes this is a Function.
–5 –4
–3 –2
–1
–1
–2
–3
1
2
3
4
5
Example 4
Determine if the graph is a function.
5
4
3
This is NOT A Function.
2
1
–5 –4
–3 –2
–1
–1
–2
–3
1
2
3
4
5
Making a mapping diagram
Example 5: Make a mapping diagram for the
relation {(-1,-2), (3,6), (-5,-10), (3,2)}
Domain
Range
-5
-10
-1
-2
3
2
6
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
f(x) is not a linear function
because it has an x2 term.
b) g(x) = -3x + 4
g(x) is a linear function.
g(3) = -3(3) + 4
f(3) = (3)2 + 4(3) - 1
f(3) = 9 + 12 – 1 = 20
g(3) = -9 + 4 = -5
Guided Practice
Due Today:
All-In-One Workbook
Practice 2-1 (4-17) all
HOMEWORK
Due Next Class:
Pg. 61 – 63
(1-25 )eoo (33-39 ,43-45)
odd, 50, 51