1. 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.

2. 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, …

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}
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

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