CHAPTER 2 Section 2.1. Objectives To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for.

Slides:

Advertisements

Similar presentations

Advertisements

MAT 105 SP09 Functions and Graphs

Think, Think, Think. Algebra I Seminar. How Much Do you Remember? The Coordinate Plane X-axis, Y-axis Slope Y-intercept Ordered Pairs Slope Intercept.

X y 1 st Quadrant2 nd Quadrant 3 rd Quadrant4 th Quadrant 13.1 – The Rectangular Coordinate System origin x-axis y-axis.

Coordinate Plane 9/20. TOOLBOX: SUMMARY: Coordinate Plane: x and y-axis used to graph equations Quadrant II (neg, pos) Quadrant I (pos, pos) x-axis Origin.

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 =

Math 025 Section 7.1 Coordinate Systems

Making a Graph! Coordinate Plane (Title) x-axis y-axis Quadrant I Quadrant II Quadrant III Quadrant IV (+,+) (+,-) (-,+) (-,-) Origin (0,0) Ordered Pair.

2.1 Functions and their Graphs p. 67. Assignment Pp #5-48 all.

UPCOMING QUIZ and TEST DATES: Wed 10/1: Quiz - Sections

COORDINATE PLANE x-axisy-axis. COORDINATE PLANE QUADRANTS III III IV (+, +)(-, +) (-, -)(+, -)

Objective The student will be able to: graph ordered pairs on a coordinate plane.

Algebra II w/ trig.  Coordinate Plane  Ordered pair: (x, y)  Relation: a set of ordered pairs(mapping, ordered pairs, table, or graphing)  Domain:

2.1 Relations and Functions. Target Goals: Identify the domain and range. Identify if a relation is a function. Evaluate functions NEW VOCABULARY.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc Basics of Functions and Their Graphs.

Copyright © 2014, 2010, 2007 Pearson Education, Inc.

Drill #16 List the relation (set of ordered pairs) and the domain and range of the following mapping: 1. Graph the following relation, state the domain.

1.1 Relations and Functions

Warm-Up Graph the point (2, -3) If

Relation Input Output Function Domain Range Scatter Plot Linear Equation x - intercept y- intercept Slope Rise Run.

Do Now 10/26/10 In your notebook, explain how you know a function is a function. Then answer if the following three tables are functions or not. x

(2-1) Relations and Functions. Cartesian Coordinate Plane Def: Composed of the x-axis (horizontal) and the y-axis (vertical) which meet at the origin.

Chapter 2 Linear Relations & Functions. 2-1 relations & functions Order pair – a pair of coordinates, written in the from ( x, y ), used to locate any.

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?

2.1 Functions and their Graphs page 67. Learning Targets I can determine whether a given relations is a function. I can represent relations and function.

Graphing With Coordinates

3-1 Symmetry and Coordinate Graphs Pre Calc A. Point Symmetry Symmetric about the origin: any point in Quadrant I has a point in Quadrant III (rotate.

Chapter 7 Section 1 The Cartesian Coordinate System and Linear Equations in Two Variables.

Drill #16 List the relation (set of ordered pairs) and the domain and range of the following mapping: Draw a mapping, and state the domain and range.

Objectives 1. To determine if a relation is a function.

Chapter 2 Section 1. Objective Students will interpret the meaning of presented data and determine if the data represents a function. They will also be.

Objective The student will be able to: 1. graph ordered pairs on a coordinate plane. 2. identify the domain and range of a relation. 3. show relations.

Section 8.2 Points, Lines and Their Graphs. Vocabulary Graph/Plot – an ordered pair or a point in a numbered plane Horizontal Axis – x-axis Vertical Axis.

Thursday. Relations and Functions Chapter 2 Section 2-1 Pages

2.1 “Relations & Functions” Relation: a set of ordered pairs. Function: a relation where the domain (“x” value) does NOT repeat. Domain: “x” values Range:

1.3 Graphing Systems of Equations Algebra II. Cartesian Coordinate Plane x-axis Quadrant IVQuadrant III Quadrant IIQuadrant I y-axis Origin x-axis (4,

 Analyze and graph relations.  Find functional values. 1) ordered pair 2) Cartesian Coordinate 3) plane 4) quadrant 5) relation 6) domain 7) range 8)

EXAMPLE 2 Plot points in a coordinate plane

 Check your grade on Student Connect  Talk to Mr. Szwast if you were absent  We will go over the test in class tomorrow.

2-1 Relations and Functions Objective: To graph a relation, state its domain and range, and determine if it is a function, and to find values of functions.

Chapter 3: Functions and Graphs Section 3.1: The Coordinate Plane & Section 3.2: Relations and Functions.

Drill #10 List the relation (set of ordered pairs) and the domain and range of the following mapping: 1. Find the value of the following if f(x) = 2.f(

Do Now 10/22/09 Copy HW in your planner. Copy HW in your planner. Text p. 209, #4-32 even & 36, 38 Text p. 209, #4-32 even & 36, 38 Take out HW from last.

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.

Linear Functions and Graphs Student Study Guide Mrs. Robertson May 2012.

Chapter 2 Linear Equations and Functions. Sect. 2.1 Functions and their Graphs Relation – a mapping or pairing of input values with output values domain.

Relations and Functions.  Ordered Pair- A pair of coordinates, written in the form (x,y), used to locate any point on a coordinate plane.  Cartesian.

4.1 NOTES. x-Axis – The horizontal line on the coordinate plane where y=0. y-Axis – The vertical line on the coordinate plane where x=0.

2-1: Graphing Linear Relations and Functions

Graphs and Applications of Linear Equations

1-6 Relations Goals: Represent relations as tables, ordered pairs, graphs and mappings. Eligible Content: A / A / A / A

Relations and Functions

2.1 Relations and Functions

Graphing in the Coordinate Plane

2-1: Graphing Linear Relations and Functions

Functions and their Graphs

Graphing Linear Relations and Functions

2-1: Graphing Linear Relations and Functions

2-1: Graphing Linear Relations and Functions

2.1 Represent Relations and Functions

2.1 Functions and Their Graphs

2-1: Graphing Linear Relations and Functions

Graphing Linear Relations and Functions

RELATIONS & FUNCTIONS CHAPTER 4.

1-6 Relations Goals: Represent relations as tables, ordered pairs, graphs and mappings. Eligible Content: A / A / A / A

Graphing Linear Relations and Functions

Differentiating between relations and functions

Name the quadrant or the axis on which the following points lie.

Presentation transcript:

CHAPTER 2 Section 2.1

Objectives To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for a given elements of the domain. Use a graphing calculator to graph linear equations Why is it important? You can use relations to solve problems involving geography, forestry, and sports.

Coordinate System What is a coordinate system? A system that uses coordinates to establish position. What are some examples? Graphs Latitude/Longitude

Cartesian Coordinate Plane What are the different components of this coordinate plane? x-axis y-axis origin ordered pairs quadrants (x, y) III III IV

Relation A set of ordered pairs, (x, y), forms a relation. Domain- all the x values Range – all the y values

Mapping {(2, 3), (-4, 8), (2, 6), (7, -3)} What is the domain? Range

Functions A function is a special type of relation in which each element of the domain is paired with exactly one element from the range. Which of the following are functions?

Vertical Line Test Which relations were functions? What is the vertical line test?

Continuous Function What do we think it means? Contains points that are connected *This means NO gaps

Discrete Function What do we think it means? Contains points that are NOT connected

Examples State Whether each relation is a function or not xy (4,-1) (2,3) (2,2) (3,1) Function Not a Function

Examples For each relation: - state the domain and range. - identify whether it is a function or not - state whether it is discrete or continuous a) {(7, 8), (7, 5), (7, 2), (7,-1)} b) y = -2x + 1 c) {(6, 2.5), (3, 2.5), (4, 2.5)} Domain: {7}; Range: {8, 5, 2, -1}; Not a Function Domain: All Reals; Range: All Reals; Function; Continuous Domain: {3, 4, 6}; Range: {2.5}; Function; Discrete

Examples Find f(5) if f(x) = x 2 – 3x f(5) = 5 2 – 3(5) f(5) = 25 – 15 f(5) = 10 Find h(-2) if h(x) = x h(-2) = (-2) h(-2) = h(-2) = -7

Graphing Technology On your graphing calculator, graph y-2x = 3 How do we do this? 1. Put function in “y =” form. y = 2x Enter Y = 2x + 3 Zoom (#6) GRAPH 3. How can we describe the graph?

Graphing Technology Now try y = -x + 14 What happens?

Exercises On the back of your notes do 1-8 (even) on page 72.

Exit Slips Remember our objectives: To graph a relation, state its domain and range, and determine if it is a function. To find values of functions for a given elements of the domain. Use a graphing calculator to graph linear equations Use them to answer your exit slip questions.