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Warm-up
• 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
• 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 Functionsvs
Discrete FunctionsDomain 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
x
y
4
-4
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.
Domain
Range
x
y
– 1
1
Example: Find the domain and range of the function f (x) = from its graph.
The domain is [–3,∞).
The range is [0,∞).
3x +
Range
Domain
(–3, 0)
Example 1Domain( , )−∞ ∞
Range[ 3, )− ∞
Example 2
Domain( , )−∞ ∞
Range( , 4]−∞
Example 3
Domain[0, )∞
Range( , )−∞ ∞
8
6
4
2
-2
-4
-6
-8
-10 -5 5 10
Domain( , )−∞ ∞
Range[2, )∞
6
4
2
-2
-4
-6
-5 5
Domain( ,3]−∞
Range[1, )∞
Domain( , )−∞ ∞
Range[0, )∞
Domain[0, )∞
Range[0, )∞
Domain( , 1) [1,6]U−∞ −
Range( ,6)−∞
Homework
• WS 1-5: Domain and Range
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