1 Linear and Nonlinear Functions How do you identify, compare, and contrast functions as linear or nonlinear? SPI 0806.3.7/ CC 8.F.3.

Slides:

Advertisements

Similar presentations

Linear and Nonlinear Functions

Advertisements

X-and Y-intercepts. Standard Form (of a linear equation) ax + by = c, where a, b, and c are integers.

Graphing Linear Equations In Slope-Intercept Form.

Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. April 27, 2015.

Graphing Linear Equations. Identifying a Linear Equation A linear equation is any equation that can be put in the form... Ax + By = C... where A, B, and.

Identify Linear, Quadratic, and Exponential Functions N Distinguish quadratic and exponential functions as nonlinear using a graph and/or a table.

The point-slope form of a linear equation of a non- vertical line is given by: Point-Slope Form of a Linear Equation.

4-2 Make a function table and a graph for the function y = –9x2. Is the function linear or nonlinear? Step 1 Make a function table using the rule y =

Matrices and Systems Engineering Frank Lipsky copyrighted.

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

Warm Up #10 1.) Graph 5x + 7y =35 2.) Graph y= 2x -3.

Identify Linear Relationships. Linear Relationship – a relationship between two quantities that have a constant rate of change. when graphed it forms.

Get out your Linear Graphic Organizer and fill it in using the slides.

Identify linear functions and linear equations. Graph linear functions that represent real-world situations. Clear Targets Linear Functions.

Linear Equations Complete the table: xy

LINEAR SYSTEMS – Graphing Method In this module, we will be graphing two linear equations on one coordinate plane and seeing where they intersect. You.

 When given a table of data related to a straight line, writing the equation of the line in slope-intercept form is very straight forward.

LEARNING TARGETS: 1. TO IDENTIFY SLOPE FROM A TABLE OF VALUES. 2. TO IDENTIFY SLOPE FROM A GRAPH. 3. TO IDENTIFY SLOPE FROM 2 POINTS. 4. TO IDENTIFY SLOPE.

Chapter 2 Graphing and Writing Linear Equations. 2.1 Graphing Linear Equations.

Linear Functions. Compare and Contrast Yards to Feet Number of Feet Number of Yards Yards to Square Yards Length of a Side of a Square Yard Area of Square.

Objectives: Represent linear patterns with equations. Represent linear equations with graphs. Standards Addressed: G: Represent relationships with.

Lesson 3.2 Topic/ Objective: Comparing linear and nonlinear functions. EQ: How can you tell if a function is linear or not? Linear Functions vs. Nonlinear.

6.4 Point-Slope Form and Writing Linear Equations Point-Slope Form of a Linear Equation –The point-slope form of the equation of a non- vertical line that.

Section 6-: Point-slope Form of a Linear Equation SPI 22C: select the graph that represents a given linear function Objective: Graph and write linear equations.

When an equation is in slope-intercept form: Examples: Identify the slope of the line and the y- intercept for each equation. 1. y = 3x y = ½.

GraphsTablesEquationsVocabularyFunctions.

TLW identify linear equations and intercepts.

Comparing Functions and Identifying Linear and Non-linear Functions

12-6 Nonlinear Functions Course 2.

Linear Expressions Chapter 3. What do you know about Linear Relations?

5.3 Standard Form of a Line Finding an Equation Given Two Points Write the equation of the line which contains: (-2, 3) (4, 5) Slope (m)=

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.

Introduction To Slope. Slope is a measure of Steepness.

7.3 Linear Equations and Their Graphs Objective: To graph linear equations using the x and y intercepts To graph horizontal and vertical lines.

Entry Task 1.Evaluate 2xy + 3(x + y) when x = 4 and y = 7 Evaluate when a = -3 and b = ab 3. 12a + (b - a - 4)

Graphing Linear Equations

Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations.

Functions LINEAR AND NON LINEAR. Linear function What is the function that states that the range values are 2 more than the domain values?  f(x) = x.

Algebra 1 Foundations, pg 338  Students will be able to write and graph linear equations using point-slope form.

Linear and Nonlinear Functions

Linear and Nonlinear Functions

Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Irma Crespo 2010.

Linear and Nonlinear Functions

Graphing Linear Inequalities

3.1 Graphing Linear Equations

Linear vs. Nonlinear Functions!

Do now Complete the table below given the domain {-1, 0, 1, 2} X

Linear Functions SOL 8.14, SOL 8.16, SOL 8.17.

Bellwork 1) How do you know if something represents a function or not?

Linear vs. Non Linear:.

Linear and Nonlinear Relationships

Equations as Relations

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.

EXIT TICKET: Graphing Linear Equations 11/17/2016

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

3.1 Graphing Linear Equations

5.1 Solving Systems of Equations by Graphing

Linear Functions Length of a Side of a Square Yard Compare and Contrast Yards to Feet Number of Feet Number of Yards Yards to Square Yards Length.

Graphing Linear Equations

Linear and Nonlinear Functions

Objective The student will be able to:

Objective The student will be able to:

Solutions of Linear Functions

Linear and Nonlinear Functions

Unit 7 More Functions: LT 7.1B - Solving for y

Linear and Nonlinear Systems of Equations

Linear and Nonlinear Systems of Equations

Aim: How do we graph lines using a table?

Linear Equations & Graphing

Lesson 4.1: Identifying linear functions

Presentation transcript:

1 Linear and Nonlinear Functions How do you identify, compare, and contrast functions as linear or nonlinear? SPI / CC 8.F.3

 Linear Functions have graphs that are straight lines and represent constant rate of change.

 Nonlinear Functions have graphs that are not straight lines.  The rate of change is not constant (values don’t increase/decrease at the same rate).

 Linear Functions represent constant rate of change.

 Nonlinear Functions do not represent constant rate of change.

XY

XY

14 x y 1086

15 In slope-intercept form, x may not be raised to a power higher than 1. X may not appear in the denominator of a fraction. No additional symbols with the x. y = x + 4 y = 6/x y = 4 y = x y = ½ x linear nonlinear linear nonlinear linear

16 y =.6x 1

17 y = 2/x + 5

18 y = x 2 + 8

19 Y = 2/x + 1

20 Let's Review!!!

A. B. Course Nonlinear Functions

C. D. Course Nonlinear Functions

y E. F. x – x y Course Nonlinear Functions

y G. H. x – x y Course Nonlinear Functions

I. InputOutput Course Nonlinear Functions

J. InputOutput Course Nonlinear Functions

K. InputOutput Course Nonlinear Functions

L. InputOutput Course Nonlinear Functions

29 Course Nonlinear Functions M.

30 Course Nonlinear Functions N.

31 Course Nonlinear Functions O. 5/x - 15 = y

32 Course Nonlinear Functions P. 6x + 2 = y

33 Exit Slip Identify if linear or nonlinear AND WHY. 1.Table A 2.Graph 3.Equation x y 1086 abc y = x