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**Chapter 1: Number Patterns 1.1: Real Numbers, Relations, and Functions**

Essential Question: What are the subsets of the real numbers? Give an example of each.

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**1.1: Real Numbers, Relations, and Functions**

Natural Numbers: Whole Numbers: Integers: Rational Numbers: Can be expressed as a ratio Irrational Numbers: No way to simplify the number Non-terminating, non-repeating decimals 1, 2, 3, 4 … 0, 1, 2, 3, 4 … … -3, -2, -1, 0, 1, 2, 3, …

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**1.1: Real Numbers, Relations, and Functions**

All real numbers are either rational or irrational Rational Numbers Integers Whole Numbers Natural Numbers Irrational Numbers

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**1.1: Real Numbers, Relations, and Functions**

Cartesian plane: another name for the coordinate plane Numbers are placed on the coordinate plane using ordered pairs Ordered pairs are in the form (x, y) Scatter plot → Data placed on a coordinate plane Domain of a relation → possible x values Range of a relation → possible y values

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**1.1: Real Numbers, Relations, and Functions**

Example 2: Domain and Range of a Relation Find the relation’s domain and range Answer: We can use the ordered pair (height, shoe size) for our relation. This give us 12 ordered pairs: (67,8.5),(72,10),(69,12),(76,12),(67,10),(72,11), (67,7.5),(62.5,5.5),(64.5,8),(64,8.5),(62,6.5),(62,6) Domain: {62, 62.5, 64, 64.5, 67, 69, 72, 76} Range: {5.5, 6, 6.5, 7.5, 8, 8.5, 10, 11, 12} Height (inches) 67 72 69 76 62.5 64.5 64 62 Shoe size 8.5 10 12 11 7.5 5.5 8 6.5 6

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**1.1: Real Numbers, Relations, and Functions**

Functions → a method where the 1st coordinate of an ordered pair represents an input, and the 2nd represents an output Each input corresponds to one AND ONLY ONE output Example 4: Identifying a Function Represented Numerically {(0,0),(1,1),(1,-1),(4,2),(4,-2),(9,3),(9,-3)} {(0,0),(1,1),(-1,-1),(4,2),(-4,2),(9,3),(-9,3)} {(0,0),(1,1),(-1,-1),(4,2),(-4,-2),(9,3),(-9,-3)}

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**1.1: Real Numbers, Relations, and Functions**

Example 5: Finding Function Values from a Graph / Figure 1.1-8 On board Functional Notation f(x) denotes the output of the function f produced by the input x y= f(x) read as “y equals f of x”

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**1.1: Real Numbers, Relations, and Functions**

Functional Notation f = name of function x = input number f(x) = output number = = directions on what to do with the input

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**1.1: Real Numbers, Relations, and Functions**

Functional Notation (Example 6) For h(x) = x2 + x – 2, find each of the following h(-2) = (-2)2 + (-2) – 2 = 4 – 2 – 2 = 0 h(-a) = (-a)2 + (-a) – 2 = a2 – a – 2

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**1.1: Real Numbers, Relations, and Functions**

Assignment Page 10-12 1-33, odd problems

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