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Unit 1: Functions Lesson 4: Domain and Range Learning Goals: I can determine domains and ranges for tables, graphs, equations, and real world situations I can describe domain and range using set notation.

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Unit 1: Functions Lesson 4: Domain and Range Natural Numbers – These are the sort of numbers you can count on your fingers. ex. 1, 2, 3,… We give them the symbol N.

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Unit 1: Functions Lesson 4: Domain and Range Whole Numbers – All the Natural Numbers, but also includes zero. ex. 0, 1, 2, 3, … We give them the symbol W.

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Unit 1: Functions Lesson 4: Domain and Range Integer Numbers – or just Integers – All the Whole Numbers, including their negative versions. ex. …-3, -2, -1, 0, 1, 2, 3,… We give them the symbol Z.

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range Real Numbers - All Rational and Irrational Numbers. We give them the symbol. (A fancy looking R).

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range Set Notation - A collection of things, called elements Example: The set notation for things in my pencil case is:

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Unit 1: Functions Lesson 4: Domain and Range “my pen" is an element of, and thus belongs to, the "Things in my Pencil Case" set

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Unit 1: Functions Lesson 4: Domain and Range We can use set notation to represent a set of numbers. For example: { 1, 2, 3, 5, 7, 11, 13….}

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range To summarize: { variable | restriction(s), variable type }

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Unit 1: Functions Lesson 4: Domain and Range The following example shows numbers that ARE included in a set: The closed dots indicate that 2 and 6 are included in the set. The straight brackets indicate the 2 and 6 are included in the set

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Unit 1: Functions Lesson 4: Domain and Range The following example shows numbers that are NOT included in a set: The open dots indicate that 2 and 6 are not included in the set. The round brackets indicate the 2 and 6 are not included in the set

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Unit 1: Functions Lesson 4: Domain and Range The arrow indicates that all numbers bigger than 3 are included in this set

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Unit 1: Functions Lesson 4: Domain and Range What does that mean?

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Unit 1: Functions Lesson 4: Domain and Range Can you graph it?

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Unit 1: Functions Lesson 4: Domain and Range Inequalities Symbols > (greater than) < (less than) ≤ (less than or equal to) ≥ (greater than or equal to) (remember to read inequalities from left ---> right) ex: 5 > 2 means Five is greater than 2

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Graphs

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Graphs

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Graphs

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Graphs

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Equations – Linear Y = -3x + 7

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Unit 1: Functions Lesson 4: Domain and Range Determining Domain and Range from Equations – Quadratic f(x) = 2x 2 – 3x + 1

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range Sometimes there will be additional restrictions when our equations are representing real life situations.

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Unit 1: Functions Lesson 4: Domain and Range Let’s see where the ball is after 3 seconds: h(3) = -5(3) 2 + 20(3) h(3) = -5(9) + 60 h(3) = -45 + 60 h(3) = 15 m

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range

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Unit 1: Functions Lesson 4: Domain and Range Homework Level 4: Pg. 35-37 #1 – 11, 13-15 Level 3: Pg. 35-37 #1 – 11, 13 Level 2: Pg. 35-37 # 1 – 7 Level 1: Pg. 35-37 #1 - 4

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