Chapter 1 – Lesson 1 Real Numbers, Relations, and Functions

Real Numbers = {every # you can think of} Rational = number that can be expressed as ratio (includes terminating decimals & repeating) Irrational = nonterminating, non repeating Integers = …,-2, -1, 0, 1, 2, … Natural Number = 1, 2, 3, 4, …{Counting} Whole Numbers = 0, 1, 2, 3, 4, …. Real Numbers Rational Whole Integers Natural Irrational

The Real Number Line

The Coordinate/Cartesian Plane AKA  Rectangular Origin (0,0) The Point (3,-4) x-coordinate y-coordinate Discuss Scatter Plots

A Relation and Its Domain Relation = The first variable is related to the second (x, y) Domain = Possible values for x Range = Possible values that y can have Check out example 2 on page 6 Rules of Relations

Functions Function = set of ordered pairs in which the first coordinate denotes the input, the second coordinate denotes the output that is obtained from the rule of the function. –Each input corresponds to one and only one output! –Example 5 on page 8

Function Notation f(a) denotes the output of the function f produced by input a So, f(x) = y is read as “f of x equals y” f(x) = x Name of function Tells you what to do with input number to get output Output number Input Number

Example g(x) = x 2 – 2x + 1 a.g(-3) = ? b.g(-r) = ? c.g(√2) = ?

Example g(x) = x 2 – 2x + 1 a.g(-3) = 16 b.g(-r) = r 2 + 2r + 1 c.g(√2) = 3 - 2√2