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

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. 1.1: Real Numbers, Relations, and Functions. Real Numbers Natural Numbers: Whole Numbers: Integers:

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

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  1. Chapter 1: Number Patterns1.1: Real Numbers, Relations, and Functions Essential Question: What are the subsets of the real numbers? Give an example of each.

  2. 1.1: Real Numbers, Relations, and Functions • Real Numbers • 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, …

  3. 1.1: Real Numbers, Relations, and Functions • All real numbers are either rational or irrational • Rational Numbers • Integers • Whole Numbers • Natural Numbers • Irrational Numbers

  4. 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

  5. 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}

  6. 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)}

  7. 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”

  8. 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

  9. 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

  10. 1.1: Real Numbers, Relations, and Functions • Assignment • Page 10-12 • 1-33, odd problems

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