Warm-up
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1. Given this relation:
{(2, -1), (4, -1), (3, 2), (5, 1), (4, 2), (5, 1)}
Domain?
Range?
Function or Not? Explain why?
2. Convert these to Interval Notation
x<6
2≤ x<5
Warm-up
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1. Given this relation:
{(2, -1), (4, -1), (3, 2), (5, 1), (4, 2), (5, 2)}
Domain? {2,3,4,5}
Range? {-1,1,2}
Function or Not? NO, duplicated “x” values
• 2.
• x < 6 in interval notation (-∞, 6)
• 2 ≤ x < 5 in interval notation [2, 5)
Continuous Functions
vs
Discrete Functions
Domain and Range
Chapter 2
Section 2-1
Pages 72-81
Objectives
•I can determine Domain
and Range from a
Continuous Graph
•I can identify a discrete
and continuous function
Important Vocabulary
•Discrete Function
•Continuous Function
Discrete Function
• A function with ordered
pairs that are just points
and not connected.
Discrete Function
Continuous Functions??
• A function is continuous if it has an infinite
domain and forms a smooth line or curve
• Simply put: It has NO BREAKS!!!
• You should be able to trace it with your
pencil from left to right without picking up
your pencil
8
The domain of the function y = f (x) is the set of
values of x for which a corresponding value of y exists.
The range of the function y = f (x) is the set of values of
y which correspond to the values of x in the domain.
y
Range
x
4
-4
Domain
Example: Find the domain and range of the
function f (x) =
x  3 from its graph.
y
Range (–3, 0)
1
–1
Domain
The domain is [–3,∞).
The range is [0,∞).
x
Example 1
Domain
(, )
Range
[3, )
Example 2
Domain
(, )
Range
(, 4]
Example 3
Domain
[0, )
Range
(, )
8
Domain
6
(, )
4
Range
2
[2, )
-5
5
-2
Domain
6
4
(,3]
Range
[1, )
2
-5
5
Domain
(, )
Range
[0, )
Domain
[0, )
Range
[0, )
Domain
(, 1) U [1, 6]
Range
(, 6)
Homework
• WS 1-5: Domain and Range