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