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

Slides:

Advertisements

Similar presentations

Introduction to Functions

Advertisements

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 =

EXAMPLE 3 Write an equation for a function

Section 1.2 Basics of Functions

Objective - To graph linear equations using x-y charts. One Variable Equations Two Variable Equations 2x - 3 = x = 14 x = 7 One Solution.

Functions. A function is a relation that has exactly one output for each input.

4.2 Graphing linear equations Objective: Graph a linear equation using a table of values.

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

SECTION 5.1a Linear Functions and Graphs. A ________ is a set of __________________. relationordered pairs Relation = { (3,5),(-2,8),(-3,8),(0,-6) } The.

Bell Quiz. Objectives Make graphs and decide if they represent functions.

1.1 Relations and Functions

4-1 Identifying Linear Functions

Is this relation a function? Explain. {(0, 5), (1, 6), (2, 4), (3, 7)} Draw arrows from the domain values to their range values.

Formalizing Relations and Functions

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

Graph each point on the same coordinate plane. 1. A(-1,2) 2. B(4,7) 3. C(-3,0) 4. D(0,3) 5. Refer to Exercises 1-4. Which equation below gives the relationship.

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.

Section 2.2 Functions  Functions & Graphs  Function Notation & Equations  Applications: Interpolation & Extrapolation 12.2.

Class 5: Question 1 Which of the following systems of equations can be represented by the graph below?

Functional Relationships

Holt Algebra Identifying Linear Functions Warm Up 1. Solve 2x – 3y = 12 for y. 2. Graph for D: {–10, –5, 0, 5, 10}.

2.3 Introduction to Functions

2.3 – Introduction to Functions  Objectives:  State the domain and range of a relation, and tell whether it is a function.  Write a function in function.

8.1-2 – Exponential Functions. Ex. 1 Sketch the graph of y = 2 x. Then state the functions domain & range.

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:

9.2 Relations CORD Math Mrs. Spitz Fall Objectives Identify the domain, range and inverse of a relation, and Show relations as sets of ordered pairs.

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.

Section 2.1 Notes: Relations and Functions

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.

SOLUTION EXAMPLE 1 Represent relations Consider the relation given by the ordered pair (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1). a. Identify the.

9.5 Functions CORD Math Mrs. Spitz Fall Objectives Determine whether a given relation is a function, and Calculate functional values for a given.

Write a function rule for a graph EXAMPLE 3 Write a rule for the function represented by the graph. Identify the domain and the range of the function.

Lesson 31 Relations and Functions NCSCOS Obj.: 2.01 Daily Objectives TLW identify the domain and range of a relation. TLW show relations as sets and mappings.

Graphing Linear Equations 4.2 Objective 1 – Graph a linear equation using a table or a list of values Objective 2 – Graph horizontal or vertical lines.

Goal: Identify and graph functions..  Relation: mapping or pairing, of input values with output values.  Domain: Set of input values.  Range: set of.

EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph.

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.

1 The graph represents a function because each domain value (x-value) is paired with exactly one range value (y-value). Notice that the graph is a straight.

Algebra 2 Foundations, pg 64  Students will be able to graph relations and identify functions. Focus Question What are relations and when is a relation.

Algebra 2 June 18, 2016 Goals:   Identify functions in coordinate, table, or graph form   Determine domain and range of given functions.

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.

Notes:Relations and Functions Section 1-6 Student Objective: The students will be able to identify relations and functions and evaluate functions. 1.Definitions:

Graphing Linear Relations and Functions

Relations and Functions

Relations and Functions

Functions Unit 8.

6-6 Systems of Linear Inequalities

Inverse functions and Relations

8-1: Relations and Functions

4.8 Functions and Relations

EXAMPLE 1 Represent relations

Notes Over 4.2 Is a Solution Verifying Solutions of an Equation

Introduction to Functions

1.7 Represent Graphs as Functions

Objectives Identify linear functions and linear equations.

Objectives Identify linear functions and linear equations.

4 minutes Warm-Up Determine the coordinates of each point in the graph below x y A B C D.

Relations for functions.

Objectives The student will be able to:

5.1 Solving Systems of Equations by Graphing

Drill 1) What quadrant would each point be located in:

Relations & Functions.

Solutions of Linear Functions

RELATIONS & FUNCTIONS CHAPTER 4.

Make a table and a graph of the function y = 2x + 4

Objectives The student will be able to:

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

I can determine whether a relation is a function

Objectives The student will be able to:

Presentation transcript:

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

Definitions Domain: first coordinates in a set of ordered pairs, x values (3, 4), (5, 6) - Domain = 3, 5 Range: second coordinates in a set of ordered pairs, y values (3, 4), (5, 6) - Range = 4, 6 Function: Pairing between two sets of numbers in which each element of the first set is paired with exactly one element of the second set

Exercises: Determine the domain and range of each relation. 5. (2, 9), (3, 10), (5, 12), (9, 14) Domain: 2, 3, 5, 9 Range: 9, 10, 12, (0, 17), (7, -12), (13, 21), (18, 40) Domain: 0, 7, 13, 18 Range: 17, -12, 21, (2, 9), (3, 10), (5, 12), (9, 14)

Exercises: Determine whether each relation is a function 1. (12, 7), (6, 5), (12, -7), (6, -5) When two x values are the same, it is NOT a function. Domain: 12 and 12 Use the vertical line test to see if it is a function

Exercises: Determine whether each relation is a function 3. (1, 3), (2, 3), (4,3), (5,3) (6, 3) When two y values are the same, it IS a function. Range: 3 Use the vertical line test to see if it is a function

5.1 Linear Functions and Graphs Practice Masters Level B

For each relation, (a) describe the domain, (b) describe the range, and (c), determine whether the relation is a function 1. (8, 12.5), (10, 12.3), (15, 12.1) a. Domain: 8, 10, 15 b. Range: 12.5, 12.3, 12.1 c. Function

Complete each ordered pair so that it is a solution to 2x - y = 10 3.(2, ___ ) 4.(___, 8) 5.(-1, ___)

The table below shows the cost for film developing. A processing fee of $2.00 is charged per roll, and there is an additional fee per picture. 9. Write an equation for the function.  Every 3 pictures increases 30 cents Number of pictures, x Cost, in dollars, y $3.20$3.50$4.40$5.60  Every 1 picture increases 10 cents  $2.00 processing fee Y = x

10. Write a set of ordered pairs for the function. (12, 3.20) Number of pictures, x Cost, in dollars, y $3.20$3.50$4.40$5.60 (15, 3.50) (24, 4.40) (36, 5.60)

11. Identify the domain shown in the table. 12, 15, 24, 36 Number of pictures, x Cost, in dollars, y $3.20$3.50$4.40$5.60

12. Identify the range shown in the table. 3.20, 3.50, 4.40, 5.60 Number of pictures, x Cost, in dollars, y $3.20$3.50$4.40$5.60

13. The graph below shows a linear function. Complete the table of values, and determine an equation of the line. Y = 2x + 1 XY XY