1.1 Relations and Functions

Slides:



Advertisements
Similar presentations
2-1: Graphing Linear Relations and Functions
Advertisements

Algebra 4-6 Functions Functions
ON TARGET REVIEW LAST WEEK Review. ON TARGET Determine whether each equation is a linear equation. If so, write the equation in standard form. 1. xy =
Section 1.2 Basics of Functions
Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Basics of Functions and Their Graphs.
4-1: Relations and Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
A function from a set A to a set B is a relation that assigns to each element x in the set A exactly one element y in the set B. The set A is called the.
Representing Functions
Chapter 1 A Beginning Library of Elementary Functions
Relations and Functions
Drill #61 For each equation make an x,y chart and find 3 points for each equation. Plot each set of points on a coordinate plane. 1.x + y = x – y.
5.2 Relations and Functions A relation is a set of ordered pairs. The domain of a relation is the set of first coordinates of the ordered pairs – the x-
Section Functions Function: A function is a correspondence between a first set, called the domain and a second set called the range such that each.
Objective: 1-1 Relations and Functions 1 SAT/ACT Practice  1. What is the sum of the positive even factors of 12?
Relations and Functions. Review A relation between two variables x and y is a set of ordered pairs An ordered pair consist of a x and y-coordinate A relation.
5.2 Relations & Functions. 5.2 – Relations & Functions Evaluating functions Remember, the DOMAIN is the set of INPUT values and the RANGE is the set of.
Relations and Functions. Def: Relation A relation is a set of ordered pairs. The domain is the set of all abscisses (x-values) and the range is the set.
1.4 Relations & Functions. Relation: a set of ordered pairs Domain (D): set of first coordinates of the pairs Range (R): set of second coordinates of.
Remediation Notes Relation Function Every equation/graph/set of ordered pairs represents a relation, but sometimes a relation is a function. Functions.
Relations Relation: a set of ordered pairs Domain: the set of x-coordinates, independent Range: the set of y-coordinates, dependent When writing the domain.
Bell Ringer 10/30/ Objectives The student will be able to: 1. identify the domain and range of a relation. 2. show relations as sets and mappings.
Relations and Functions Algebra I. Identifying Relations and Functions A relation is a set of ordered pairs. The (age, height) ordered pairs below form.
Objectives The student will be able to:
5.2 Relations and Functions. Identifying Relations and Functions Relation: A set of ordered pairs. You can list the set of ordered pairs in a relation.
Functions Objective: To determine whether relations are functions.
2.1 Relations and Functions A relation is a set of pairs of input and output values. – There are four different ways to represent relations.
Review Functions. Function A function is a special type of relation in which each element of the domain is paired with exactly one element of the range.
Functions 4-6 I can determine whether a relation is a function and find function values. S. Calahan 2008.
2-1: Graphing Linear Relations and Functions
Graphing Linear Relations and Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Relations and Functions
CHAPTER 2 SECTION 1.
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter Functions.
1-1: Graphing Linear Relations and Functions
Do Now Complete the chart for each linear equation. y = x - 2
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Relations and Functions
Relations and Functions Pages
Bellringer Graph each ordered pair on the coordinate plane.
2-1: Graphing Linear Relations and Functions
Functions, Relations, Domain, & Range
1-1 Relations and Functions
1-1 RELATIONS & FUNCTIONS
1.7 Represent Graphs as Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc.
1.2: Graphing Linear Relations and Functions
Graphing Linear Relations and Functions
FUNCTION NOTATION AND EVALUATING FUNCTIONS
3-2 Representing Functions
Formalizing Relations & Functions
2-1: Graphing Linear Relations and Functions
2-1: Graphing Linear Relations and Functions
5.2 Relations and Functions
2-1: Graphing Linear Relations and Functions
Introduction to Functions
2-1: Graphing Linear Relations and Functions
Graphing Linear Relations and Functions
3.5 – Introduction to Functions
Functions MATHPOWERTM 11, WESTERN EDITION
Relations/Sequences Objective: Students will learn how to identify if a relation is a function. They will also be able to create a variable expression.
Section 1 – Relations and Functions
f(x) y x A function is a relation that gives a single
Graphing Linear Relations and Functions
UNDERSTANDING FUNCTIONS
3.2 Representing Functions Objectives The student will be able to:
1.4 Relations & Functions.
3 Chapter Chapter 2 Graphing.
Presentation transcript:

1.1 Relations and Functions

Relations the pairing of elements of one set to the elements of another set can be represented by ordered pairs First coordinate is the domain Second coordinate is the range can be represented as a table of values can be graphed some relations can be described by a rule or equation that relates the first and second coordinates

Windchill Factors at 20⁰ F Wind Speed (mph) Windchill Temperature (⁰F) 5 19 10 3 15 -5 20 -10 25 -15 30 -18 State the relation of the windchill data as a set of ordered pairs State the domain and range of the relation

The domain of a relation is all consecutive integers between -2 and 2 The domain of a relation is all consecutive integers between -2 and 2. The range y of the relation is 2 less than twice x, where x is a member of the domain. Write the relation as a table of values and as an equation. Then graph the relation. x y

State the domain of range of each relation.

Functions A function is a relation in which each element of the domain is paired with exactly one element in the range. The domain cannot repeat On a graph of a relation, if every vertical line drawn on the graph of a relation passes through no more than one point on the graph, then the relation is a function. This is called the vertical line test.

{(-3,-2), (-2,-2), (-1,-2), and (0,-2)} State the domain and range of each relation. Then state whether the relation is a function. {(-2,0), (3,2),(4,5)} {(-3,-2), (-2,-2), (-1,-2), and (0,-2)}

Determine whether the graph of each relation represents a function.

Function Notation f(x) is read “f of x” and should be interpreted as the value of function f at x. The expression y = f(x) indicates that for each element in the domain that replaces x, the function assigns one and only one replacement for y. The ordered pairs of a function can be written in the form (x, y) or (x, f(x)).

Evaluate each function for the given value. f(-1) if f(x) = -x³ - 1 f(3) if f(x) = g(m) if g(x) = 2x⁶ - 10x⁴ - x² + 5 h(a-2) if h(x) = 2x² – x + 3

When given the equation of a function but the domain is not specified, the domain is all real numbers for which the corresponding values in the range are also real numbers.

Homework pages 10 – 11 18, 38, 42, 44, 46 48, and 52 a, b, c You do not have to write the problems. You must follow directions and show all work.