Chapter 2 Linear Relations and Functions

Size: px
Start display at page:

Download "Chapter 2 Linear Relations and Functions"

Transcription

1 Chapter Linear Relations and Functions I. Relations and Functions A. Definitions 1. Relation. Domain the variable ( ) 3. Range the variable ( ). Function a) A relationship between ( ) and ( ). b) The output ( ) depends on the input ( ). c) A in which each element in the is mapped to and onl element in the. B. Eamples 1. Determine whether each relation is a function. a) Mappings: b) Tables: c) Ordered Pairs: {( 5,),(,5),(0,7),(0,9) }. Graphs: 1) ) 3) Note: Vertical Line Test Honors Algebra Chapter Page 1

2 C. Function Values and Notation 1. Function Notation a) = 3 8 vs. f ( ) = 3 8 b) Function notation has the advantage of clearl identifing the dependent variable f ( ), formerl known as, while at the same time telling ou is the independent variable and that the function itself is called f. c) Function notation allows ou to be less word. Instead of asking What is the value of that corresponds to =? ou can ask What is f ( )? :. Eamples 3 a) If f ( ) = 3, find f (). b) If h( ) = , find h (1.6). c) If f =, find ( ) 3 ( ) 3 f t. d) Etra: If g a =, find g( b + 3). ( ) a 6 Homework: Worksheet Section.1 Honors Algebra Chapter Page

3 II. Linear Equations A. Standard Form: a + b = c, where a, b, and c are integers. B. Intercepts 1. -intercept a) Occurs when the line crosses the. b) The equals 0. -intercept a) Occurs when the line crosses the. b) The equals 0 C. Linear equations: Note: When variables other than and are used, assume that the letter coming first in the alphabet represents the or horizontal ais. D. Eamples: 1. Write in standard form: 1 3 =. Find the intercepts and graph: + = 0 Homework: Worksheet Section. III. Slope A. Definition: B. Formula: C. Eample: Find the slope of a line that passes through the points (1,-3) and (-1,6). D. Tpes of Slopes: Homework: Worksheet Section.3 Honors Algebra Chapter Page 3

4 IV. Slope Intercept Form/Point Slope Form A. = m + b where m is the slope and b is the -intercept. B. ( ) = m( ) where (, ) 1 1 is a given point and m is the slope. 1 1 C. Find the equation of a line with the following description: 1. Slope of 3 and goes through the point of (-1,6).. Goes through the points (,-1) and (5,-8). 3. Goes through the points (3,-1) and (8,-1). D. Parallel and Perpendicular Lines 1. Parallel Slopes are.. Perpendicular Slopes are an. 3. Eamples a) Find an equation of a line that is parallel to = + 5 and goes through the point (7,1). b) Find an equation of a line that is parallel to 3 5 = 7 and goes through the point (-,5). c) Find an equation of a line that is perpendicular to = + 5 and goes through the point (,1). Homework: Worksheet. Honors Algebra Chapter Page

5 V. Modeling Real-World Data (Manuall) Tpes of correlation 1. Positive correlation. Negative correlation 3. No correlation A equation can be determined b using a process to the one used to find the of a. The procedure Eamples 1. The table below shows the approimate percent of students who sent applications to two colleges in various ears since Draw a scatter plot, best fit line, and find an equation that would predict the approimate percent of students who sent applications to two colleges in various ears since Predict the percent of students who will send applications to two colleges in 010. What is the dependent and independent variable and wh? What tpe of correlation does this data have? Safet The table below shows the approimate percent of drivers who wear seat belts in various ears since 199. What is the dependent and independent variable and wh? Draw a scatter plot and a best fit line. What tpe of correlation does this data have? Find an equation that would predict the approimate percent of drivers who wear seatbelts since 199. What do the slope and -intercept indicate? Predict the percent of drivers who will be wearing seat belts in Homework: p all, 1-8 all, 30 Honors Algebra Chapter Page 5

6 Scatter Plots and Regression (prediction) Lines 1. Entering Data a. EDIT Edit To clear a List: 1. Go to the top of list. b.. Note: Do not delete lists. Enter the -values in L1 and -values in L c. QUIT In order to get deleted lists back ou must do the following: SetUpEditor This should restore our lists.. Graphing Data We do not normall do this step, unless asked to see how well the data fits. a. Clear all equations from that do not pertain to the problem at hand. b. STAT PLOT c. Select on of the Stat Plots d. Make sure the following is selected. Note: If our - or -values are in a different list location ou can alwas change the XList: and YList: locations tping in the new list location. To select put cursor on top of item and hit You can change our mark to our preference. e. QUIT f. ZoomStat Honors Algebra Chapter Page 6

7 3. Finding the Prediction Line (Model) a. Calc LinReg(a+b) b. After LinReg(a+b) ou will need to tpe the list he -values are located (usuall L1) flowed b a comma and the list where the -values are located (usuall L) followed b another comma and then the location ou want to store the equation (usuall Y1). After all is tped in hit New wa: Y1 Old wa: Y1 thru Y9 can be located b doing the following: Y-VARS Function c. You should get the following. a is our slope and b is our -intercept. For this result the equation is = Using the model to predict If ou want to predict what will happen when is 5 New wa: Y1 (5) Old wa: Y-VARS Y1(5) Honors Algebra Chapter Page 7

8 VI. Modeling Real-World Data (Using a Calculator) Correlation Coefficient ( r ): Shows how well data are modeled b a function. Measures: When r is close to 1, When r = 0, When r Eamples 1. The table shows the median income of U.S. families for the period Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the median income in 015. Use a graphing calculator to make a scatter plot of the data. Find an equation for and graph a line of regression. Then use the equation to predict the attendance in 015. What is the correlation coefficient? What does this value tell us about our model?. The table shows the winning times for an annual dirt bike race for the period Use a graphing calculator to make a scatter plot of the data. Find and graph a line of regression. Then use the function to predict the winning time in 015. Homework: p all Honors Algebra Chapter Page 8

9 VII. Special Functions 1. Piecewise Function. Absolute Value Function: 3. Greatest Integer Function: ( integer not greater than ) = 3 Eample = or = or Eamples: Graph: 1, if 3 f ( ) = 1, if > 3 Find the Domain and Range. + 1, if > 1 f ( ) = 3, if 1 Find the Domain and Range. Pscholog: One pschologist charges for counseling sessions at the rate of $85 per hour or an fraction thereof. Draw a graph that represents this solution = = + f ( ) = 3 Find the Domain and Range. Find the Domain and Range. Homework: Worksheet Section.6 Honors Algebra Chapter Page 9

10 VIII. Parent Functions and Transformations Parent Graphs A. Constant Function: B. Identit Function: C. Absolute Value function: D. Quadratic Function: Transformations A. Translation 1. Horizontal:. Vertical: B. Reflection 1. Reflection over the -ais:. Reflection over the -ais: C. Dilation 1. Stretched verticall:. Compressed verticall: D. Eamples 1. Describe the translation in ( 1) Then graph the function. = +.. Describe the translation in =. Then graph the function. 3. Describe the reflection in =. Then graph the function.. Describe what transformations to the following function 1 f ( ) = +. Then graph the function. Homework: p all, 9, all, 1-19 all, 1, 8, 33, all, 5-58 all, 60 Honors Algebra Chapter Page 10

11 IX. Linear Inequalities Boundar Lines or. -- < or > Eamples: Is (,) a solution to 3 < 6? Graph: < < One tutoring compan advertises that it specializes in helping students who have a combined score on the SAT that is 900 or less. Write an inequalit to describe the combined scores of students who are prospective tutoring clients. Let represent the verbal score and the math score Homework: Worksheet Section.8 Honors Algebra Chapter Page 11

Algebra 2 Chapter 2 Page 1

Algebra 2 Chapter 2 Page 1 Mileage (MPGs) Section. Relations and Functions. To graph a relation, state the domain and range, and determine if the relation is a function.. To find the values of a function for the given element of

More information

Section 1.1 Solving Linear Equations and Inequalities a + 4b c

Section 1.1 Solving Linear Equations and Inequalities a + 4b c Section 1 Solving Linear Equations and Inequalities A. Evaluating Expressions Examples Evaluate the following if a = 7, b =, and c = ( a + c ) + b. a + b c B. The Distributive Property Try the Following

More information

H.Algebra 2 Summer Review Packet

H.Algebra 2 Summer Review Packet H.Algebra Summer Review Packet 1 Correlation of Algebra Summer Packet with Algebra 1 Objectives A. Simplifing Polnomial Epressions Objectives: The student will be able to: Use the commutative, associative,

More information

Chapter 1 Functions and Models

Chapter 1 Functions and Models Chapter 1 Functions and Models 1.2 Mathematical Models: A catalog of Essential Functions A mathematical model is a mathematical description of a real world situations such as the size of a population,

More information

Reteach 2-3. Graphing Linear Functions. 22 Holt Algebra 2. Name Date Class

Reteach 2-3. Graphing Linear Functions. 22 Holt Algebra 2. Name Date Class -3 Graphing Linear Functions Use intercepts to sketch the graph of the function 3x 6y 1. The x-intercept is where the graph crosses the x-axis. To find the x-intercept, set y 0 and solve for x. 3x 6y 1

More information

6.4 graphs OF logarithmic FUnCTIOnS

6.4 graphs OF logarithmic FUnCTIOnS SECTION 6. graphs of logarithmic functions 9 9 learning ObjeCTIveS In this section, ou will: Identif the domain of a logarithmic function. Graph logarithmic functions. 6. graphs OF logarithmic FUnCTIOnS

More information

The American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet

The American School of Marrakesh. Algebra 2 Algebra 2 Summer Preparation Packet The American School of Marrakesh Algebra Algebra Summer Preparation Packet Summer 016 Algebra Summer Preparation Packet This summer packet contains eciting math problems designed to ensure our readiness

More information

15.2 Graphing Logarithmic

15.2 Graphing Logarithmic _ - - - - - - Locker LESSON 5. Graphing Logarithmic Functions Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes on the graphs of f () = b and f () = log b

More information

Ready To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities

Ready To Go On? Skills Intervention 2-1 Solving Linear Equations and Inequalities A Read To Go n? Skills Intervention -1 Solving Linear Equations and Inequalities Find these vocabular words in Lesson -1 and the Multilingual Glossar. Vocabular equation solution of an equation linear

More information

1.3. Absolute Value and Piecewise-Defined Functions Absolutely Piece-ful. My Notes ACTIVITY

1.3. Absolute Value and Piecewise-Defined Functions Absolutely Piece-ful. My Notes ACTIVITY Absolute Value and Piecewise-Defined Functions Absolutel Piece-ful SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge, Create Representations, Quickwrite. Graph both = - for < 3 and = - + 7 for

More information

1.2. Characteristics of Polynomial Functions. What are the key features of the graphs of polynomial functions?

1.2. Characteristics of Polynomial Functions. What are the key features of the graphs of polynomial functions? 1.2 Characteristics of Polnomial Functions In Section 1.1, ou explored the features of power functions, which are single-term polnomial functions. Man polnomial functions that arise from real-world applications

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Chapter Maintaining Mathematical Proficienc Find the -intercept of the graph of the linear equation. 1. = + 3. = 3 + 5 3. = 10 75. = ( 9) 5. 7( 10) = +. 5 + 15 = 0 Find the distance between the two points.

More information

15.2 Graphing Logarithmic

15.2 Graphing Logarithmic Name Class Date 15. Graphing Logarithmic Functions Essential Question: How is the graph of g () = a log b ( h) + k where b > and b 1 related to the graph of f () = log b? Resource Locker Eplore 1 Graphing

More information

Example #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2).

Example #1: Write an Equation Given Slope and a Point Write an equation in slope-intercept form for the line that has a slope of through (5, - 2). Algebra II: 2-4 Writing Linear Equations Date: Forms of Equations Consider the following graph. The line passes through and. Notice that is the y-intercept of. You can use these two points to find the

More information

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED FOM 11 T GRAPHING LINEAR INEQUALITIES & SET NOTATION - 1 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) INEQUALITY = a mathematical statement that contains one of these four inequalit signs: ,.

More information

Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties

Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Unit 2, Ongoing Activity, Little Black Book of Algebra II Properties Little Black Book of Algebra II Properties Unit 2 - Polynomial Equations & Inequalities 2.1 Laws of Exponents - record the rules for

More information

Math 115: Review for Chapter 2

Math 115: Review for Chapter 2 Math 5: Review for Chapter Can ou determine algebraicall whether an equation is smmetric with respect to the - ais, the -ais, or the origin?. Algebraicall determine whether each equation below is smmetric

More information

Chapter 2.1 Relations and Functions

Chapter 2.1 Relations and Functions Analyze and graph relations. Find functional values. Chapter 2.1 Relations and Functions We are familiar with a number line. A number line enables us to locate points, denoted by numbers, and find distances

More information

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology.

Algebra II Notes Unit Five: Quadratic Functions. Syllabus Objectives: 5.1 The student will graph quadratic functions with and without technology. Sllabus Objectives:.1 The student will graph quadratic functions with and without technolog. Quadratic Function: a function that can be written in the form are real numbers Parabola: the U-shaped graph

More information

3.7 Linear and Quadratic Models

3.7 Linear and Quadratic Models 3.7. Linear and Quadratic Models www.ck12.org 3.7 Linear and Quadratic Models Learning Objectives Identif functions using differences and ratios. Write equations for functions. Perform eponential and quadratic

More information

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations.

MA.8.1 Students will apply properties of the real number system to simplify algebraic expressions and solve linear equations. Focus Statement: Students will solve multi-step linear, quadratic, and compound equations and inequalities using the algebraic properties of the real number system. They will also graph linear and quadratic

More information

Ch 3 Alg 2 Note Sheet.doc 3.1 Graphing Systems of Equations

Ch 3 Alg 2 Note Sheet.doc 3.1 Graphing Systems of Equations Ch 3 Alg Note Sheet.doc 3.1 Graphing Sstems of Equations Sstems of Linear Equations A sstem of equations is a set of two or more equations that use the same variables. If the graph of each equation =.4

More information

13.1 Exponential Growth Functions

13.1 Exponential Growth Functions Name Class Date 1.1 Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > 1 related to the graph of f () = b? Resource Locker Eplore 1 Graphing and Analzing f

More information

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions

Ready To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Read To Go On? Skills Intervention 5-1 Using Transformations to Graph Quadratic Functions Find these vocabular words in Lesson 5-1 and the Multilingual Glossar. Vocabular quadratic function parabola verte

More information

Characteristics of Linear Functions (pp. 1 of 8)

Characteristics of Linear Functions (pp. 1 of 8) Characteristics of Linear Functions (pp. 1 of 8) Algebra 2 Parent Function Table Linear Parent Function: x y y = Domain: Range: What patterns do you observe in the table and graph of the linear parent

More information

Session 4 2:40 3:30. If neither the first nor second differences repeat, we need to try another

Session 4 2:40 3:30. If neither the first nor second differences repeat, we need to try another Linear Quadratics & Exponentials using Tables We can classify a table of values as belonging to a particular family of functions based on the math operations found on any calculator. First differences

More information

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions Eponential and Logarithmic Functions 6 Figure Electron micrograph of E. Coli bacteria (credit: Mattosaurus, Wikimedia Commons) CHAPTER OUTLINE 6. Eponential Functions 6. Logarithmic Properties 6. Graphs

More information

Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet.

Ch 5 Alg 2 L2 Note Sheet Key Do Activity 1 on your Ch 5 Activity Sheet. Ch Alg L Note Sheet Ke Do Activit 1 on our Ch Activit Sheet. Chapter : Quadratic Equations and Functions.1 Modeling Data With Quadratic Functions You had three forms for linear equations, ou will have

More information

15.2 Graphing Logarithmic

15.2 Graphing Logarithmic Name Class Date 15. Graphing Logarithmic Functions Essential Question: How is the graph of g () = a log b ( h) + k where b > 0 and b 1 related to the graph of f () = log b? Resource Locker A.5.A Determine

More information

13.2 Exponential Growth Functions

13.2 Exponential Growth Functions Name Class Date. Eponential Growth Functions Essential Question: How is the graph of g () = a b - h + k where b > related to the graph of f () = b? A.5.A Determine the effects on the ke attributes on the

More information

Reminder: Univariate Data. Bivariate Data. Example: Puppy Weights. You weigh the pups and get these results: 2.5, 3.5, 3.3, 3.1, 2.6, 3.6, 2.

Reminder: Univariate Data. Bivariate Data. Example: Puppy Weights. You weigh the pups and get these results: 2.5, 3.5, 3.3, 3.1, 2.6, 3.6, 2. TP: To review Standard Deviation, Residual Plots, and Correlation Coefficients HW: Do a journal entry on each of the calculator tricks in this lesson. Lesson slides will be posted with notes. Do Now: Write

More information

Unit 10 - Graphing Quadratic Functions

Unit 10 - Graphing Quadratic Functions Unit - Graphing Quadratic Functions PREREQUISITE SKILLS: students should be able to add, subtract and multipl polnomials students should be able to factor polnomials students should be able to identif

More information

STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs

STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE. Functions & Graphs STUDY KNOWHOW PROGRAM STUDY AND LEARNING CENTRE Functions & Graphs Contents Functions and Relations... 1 Interval Notation... 3 Graphs: Linear Functions... 5 Lines and Gradients... 7 Graphs: Quadratic

More information

decreases as x increases.

decreases as x increases. Chapter Review FREQUENTLY ASKED Questions Q: How can ou identif an eponential function from its equation? its graph? a table of values? A: The eponential function has the form f () 5 b, where the variable

More information

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background

= x. Algebra II Notes Quadratic Functions Unit Graphing Quadratic Functions. Math Background Algebra II Notes Quadratic Functions Unit 3.1 3. Graphing Quadratic Functions Math Background Previousl, ou Identified and graphed linear functions Applied transformations to parent functions Graphed quadratic

More information

ab is shifted horizontally by h units. ab is shifted vertically by k units.

ab is shifted horizontally by h units. ab is shifted vertically by k units. Algera II Notes Unit Eight: Eponential and Logarithmic Functions Sllaus Ojective: 8. The student will graph logarithmic and eponential functions including ase e. Eponential Function: a, 0, Graph of an

More information

Solve the following equations. Show all work to receive credit. No decimal answers. 8) 4x 2 = 100

Solve the following equations. Show all work to receive credit. No decimal answers. 8) 4x 2 = 100 Algebra 2 1.1 Worksheet Name Solve the following equations. Show all work to receive credit. No decimal answers. 1) 3x 5(2 4x) = 18 2) 17 + 11x = -19x 25 3) 2 6x+9 b 4 = 7 4) = 2x 3 4 5) 3 = 5 7 x x+1

More information

x. 4. 2x 10 4x. 10 x

x. 4. 2x 10 4x. 10 x CCGPS UNIT Semester 1 COORDINATE ALGEBRA Page 1 of Reasoning with Equations and Quantities Name: Date: Understand solving equations as a process of reasoning and eplain the reasoning MCC9-1.A.REI.1 Eplain

More information

INTRODUCTION GOOD LUCK!

INTRODUCTION GOOD LUCK! INTRODUCTION The Summer Skills Assignment for has been developed to provide all learners of our St. Mar s Count Public Schools communit an opportunit to shore up their prerequisite mathematical skills

More information

Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 4. [Writing Linear Equations]

Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10. Unit 4. [Writing Linear Equations] Name: Teacher: Per: Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8 Unit 9 Unit 10 Unit 4 [Writing Linear Equations] Find the equation of a line that has slope m = 4 and passes through the point

More information

Graphing Equations in Slope-Intercept Form 4.1. Positive Slope Negative Slope 0 slope No Slope

Graphing Equations in Slope-Intercept Form 4.1. Positive Slope Negative Slope 0 slope No Slope Slope-Intercept Form y = mx + b m = slope b = y-intercept Graphing Equations in Slope-Intercept Form 4.1 Positive Slope Negative Slope 0 slope No Slope Example 1 Write an equation in slope-intercept form

More information

Chapter 6 Logarithmic and Exponential Functions

Chapter 6 Logarithmic and Exponential Functions Chapter 6 Logarithmic and Eponential Functions 6.1 The Definition of e Eample 1 Consider the eponential function f 1 ( ) 1 What happens to f() as gets very large? Type the function into Y=. Let Y 1 1 1/.

More information

Algebra 2 Unit 1 Practice

Algebra 2 Unit 1 Practice Algebra Unit Practice LESSON - Use this information for Items. Aaron has $ to rent a bike in the cit. It costs $ per hour to rent a bike. The additional fee for a helmet is $ for the entire ride.. Write

More information

2. Domain: The set of all abscissas (x s) of the ordered pairs (abscissa is the first element of an ordered pair)

2. Domain: The set of all abscissas (x s) of the ordered pairs (abscissa is the first element of an ordered pair) . Relations and Functions. Relation: A set of ordered pairs E:,4,,5,,, 8,4. The set of all abscissas s of the ordered pairs abscissa is the first element of an ordered pair. Range: The set of all ordinates

More information

Algebra I Calculator Activities

Algebra I Calculator Activities First Nine Weeks SOL Objectives Calculating Measures of Central Tendency SOL A.17 Organize a set of data Calculate the mean, median, mode, and range of a set of data Describe the relationships between

More information

Algebra 2 Practice Midterm

Algebra 2 Practice Midterm Name: Algebra 2 Practice Midterm Circle the letter for the correct answer. 1. A study comparing patients who received a new medicine with those who did not is. A. an observational study C. an experiment

More information

Solving Systems Using Tables and Graphs

Solving Systems Using Tables and Graphs 3-1 Solving Sstems Using Tables and Graphs Vocabular Review 1. Cross out the equation that is NOT in slope-intercept form. 1 5 7 r 5 s a 5!3b 1 5 3 1 7 5 13 Vocabular Builder linear sstem (noun) LIN ee

More information

Name Class Date. Solving by Graphing and Algebraically

Name Class Date. Solving by Graphing and Algebraically Name Class Date 16-4 Nonlinear Sstems Going Deeper Essential question: How can ou solve a sstem of equations when one equation is linear and the other is quadratic? To estimate the solution to a sstem

More information

A function from a set D to a set R is a rule that assigns a unique element in R to each element in D.

A function from a set D to a set R is a rule that assigns a unique element in R to each element in D. 1.2 Functions and Their Properties PreCalculus 1.2 FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1.2 1. Determine whether a set of numbers or a graph is a function 2. Find the domain of a function

More information

Chapter 11. Correlation and Regression

Chapter 11. Correlation and Regression Chapter 11 Correlation and Regression Correlation A relationship between two variables. The data can be represented b ordered pairs (, ) is the independent (or eplanator) variable is the dependent (or

More information

13.3 Exponential Decay Functions

13.3 Exponential Decay Functions 6 6 - - Locker LESSON. Eponential Deca Functions Teas Math Standards The student is epected to: A.5.B Formulate eponential and logarithmic equations that model real-world situations, including eponential

More information

Explore 1 Graphing and Analyzing f(x) = e x. The following table represents the function ƒ (x) = (1 + 1 x) x for several values of x.

Explore 1 Graphing and Analyzing f(x) = e x. The following table represents the function ƒ (x) = (1 + 1 x) x for several values of x. 1_ 8 6 8 Locker LESSON 13. The Base e Teas Math Standards The student is epected to: A.5.A Determine the effects on the ke attributes of the graphs of ƒ () = b and ƒ () = log b () where b is, 1, and e

More information

RELATIONS AND FUNCTIONS through

RELATIONS AND FUNCTIONS through RELATIONS AND FUNCTIONS 11.1.2 through 11.1. Relations and Functions establish a correspondence between the input values (usuall ) and the output values (usuall ) according to the particular relation or

More information

MATH 152 COLLEGE ALGEBRA AND TRIGONOMETRY UNIT 1 HOMEWORK ASSIGNMENTS

MATH 152 COLLEGE ALGEBRA AND TRIGONOMETRY UNIT 1 HOMEWORK ASSIGNMENTS 0//0 MATH COLLEGE ALGEBRA AND TRIGONOMETRY UNIT HOMEWORK ASSIGNMENTS General Instructions Be sure to write out all our work, because method is as important as getting the correct answer. The answers to

More information

Algebra 2 Semester Exam Review

Algebra 2 Semester Exam Review Algebra Semester Eam Review 7 Graph the numbers,,,, and 0 on a number line Identif the propert shown rs rs r when r and s Evaluate What is the value of k k when k? Simplif the epression 7 7 Solve the equation

More information

LESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II

LESSON #24 - POWER FUNCTIONS COMMON CORE ALGEBRA II 1 LESSON #4 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The

More information

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k

Name Class Date. Understanding How to Graph g(x) = a(x - h ) 2 + k Name Class Date - Transforming Quadratic Functions Going Deeper Essential question: How can ou obtain the graph of g() = a( h ) + k from the graph of f () =? 1 F-BF..3 ENGAGE Understanding How to Graph

More information

14.2 Choosing Among Linear, Quadratic, and Exponential Models

14.2 Choosing Among Linear, Quadratic, and Exponential Models Name Class Date 14.2 Choosing Among Linear, Quadratic, and Eponential Models Essential Question: How do ou choose among, linear, quadratic, and eponential models for a given set of data? Resource Locker

More information

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs

Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Ch 5 Alg Note Sheet Ke Chapter 5: Quadratic Equations and Functions 5.1 Modeling Data With Quadratic Functions Quadratic Functions and Their Graphs Definition: Standard Form of a Quadratic Function The

More information

LESSON 4.3 GRAPHING INEQUALITIES

LESSON 4.3 GRAPHING INEQUALITIES LESSON.3 GRAPHING INEQUALITIES LESSON.3 GRAPHING INEQUALITIES 9 OVERVIEW Here s what ou ll learn in this lesson: Linear Inequalities a. Ordered pairs as solutions of linear inequalities b. Graphing linear

More information

First Semester Final Review NON-Graphing Calculator

First Semester Final Review NON-Graphing Calculator Algebra First Semester Final Review NON-Graphing Calculator Name:. 1. Find the slope of the line passing through the points ( 5, ) and ( 3, 7).. Find the slope-intercept equation of the line passing through

More information

Pure Math 30: Explained!

Pure Math 30: Explained! Pure Math 30: Eplained! www.puremath30.com 9 Logarithms Lesson PART I: Eponential Functions Eponential functions: These are functions where the variable is an eponent. The first type of eponential graph

More information

MPM2D - Practice Mastery Test #5

MPM2D - Practice Mastery Test #5 MPM2D - Practice Mastery Test #5 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. 2. If, then x = a. -4 b. -3 c. 1 d. 2 3. Simplify 4. Select the table

More information

1.2 Functions and Their Properties PreCalculus

1.2 Functions and Their Properties PreCalculus 1. Functions and Their Properties PreCalculus 1. FUNCTIONS AND THEIR PROPERTIES Learning Targets for 1. 1. Determine whether a set of numbers or a graph is a function. Find the domain of a function given

More information

Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Final Exam Review. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Final Eam Review Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Determine whether or not the relationship shown in the table is a function.

More information

Algebra 2 Honors Summer Packet 2018

Algebra 2 Honors Summer Packet 2018 Algebra Honors Summer Packet 018 Solving Linear Equations with Fractional Coefficients For these problems, ou should be able to: A) determine the LCD when given two or more fractions B) solve a linear

More information

Pre-AP Algebra 2 Lesson 1-1 Basics of Functions

Pre-AP Algebra 2 Lesson 1-1 Basics of Functions Lesson 1-1 Basics of Functions Objectives: The students will be able to represent functions verball, numericall, smbolicall, and graphicall. The students will be able to determine if a relation is a function

More information

13.2 Exponential Decay Functions

13.2 Exponential Decay Functions 6 6 - - Locker LESSON. Eponential Deca Functions Common Core Math Standards The student is epected to: F.BF. Identif the effect on the graph of replacing f() b f() + k, kf(), f(k), and f( + k) for specific

More information

Maintaining Mathematical Proficiency

Maintaining Mathematical Proficiency Name Date Chapter 3 Maintaining Mathematical Proficienc Plot the point in a coordinate plane. Describe the location of the point. 1. A( 3, 1). B (, ) 3. C ( 1, 0). D ( 5, ) 5. Plot the point that is on

More information

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression

Glossary. Also available at BigIdeasMath.com: multi-language glossary vocabulary flash cards. An equation that contains an absolute value expression Glossar This student friendl glossar is designed to be a reference for ke vocabular, properties, and mathematical terms. Several of the entries include a short eample to aid our understanding of important

More information

Rising HONORS Algebra 2 TRIG student Summer Packet for 2016 (school year )

Rising HONORS Algebra 2 TRIG student Summer Packet for 2016 (school year ) Rising HONORS Algebra TRIG student Summer Packet for 016 (school ear 016-17) Welcome to Algebra TRIG! To be successful in Algebra Trig, ou must be proficient at solving and simplifing each tpe of problem

More information

UNIT 2 QUADRATIC FUNCTIONS AND MODELING Lesson 2: Interpreting Quadratic Functions Instruction

UNIT 2 QUADRATIC FUNCTIONS AND MODELING Lesson 2: Interpreting Quadratic Functions Instruction Prerequisite Skills This lesson requires the use of the following skills: knowing the standard form of quadratic functions using graphing technolog to model quadratic functions Introduction The tourism

More information

136 Maths Quest 10 for Victoria

136 Maths Quest 10 for Victoria Quadratic graphs 5 Barr is a basketball plaer. He passes the ball to a team mate. When the ball is thrown, the path traced b the ball is a parabola. Barr s throw follows the quadratic equation =.5 +. +.5.

More information

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED

MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED FOM 11 T1 SYSTEMS OF LINEAR INEQUALITIES 1 MATH SPEAK - TO BE UNDERSTOOD AND MEMORIZED 1) A SYSTEM OF LINEAR INEQUALITIES = a problem where or more inequalities are graphed on the same grid, the solution

More information

CHAPTER 1 Functions and Their Graphs

CHAPTER 1 Functions and Their Graphs PART I CHAPTER Functions and Their Graphs Section. Lines in the Plane....................... Section. Functions........................... Section. Graphs of Functions..................... Section. Shifting,

More information

Algebra 1 Skills Needed to be Successful in Algebra 2

Algebra 1 Skills Needed to be Successful in Algebra 2 Algebra 1 Skills Needed to be Successful in Algebra A. Simplifing Polnomial Epressions Objectives: The student will be able to: Appl the appropriate arithmetic operations and algebraic properties needed

More information

Section 3.1 Solving Linear Systems by Graphing

Section 3.1 Solving Linear Systems by Graphing Section 3.1 Solving Linear Sstems b Graphing Name: Period: Objective(s): Solve a sstem of linear equations in two variables using graphing. Essential Question: Eplain how to tell from a graph of a sstem

More information

2-1: Relations and Functions. Mr. Gallo Algebra 2. What is a Relation

2-1: Relations and Functions. Mr. Gallo Algebra 2. What is a Relation -1: Relations and Functions Mr. Gallo Algebra What is a Relation 1 In 000, the 4 most populous states(in millions), were CA {3}, TX {1}, NY {19} and FL {16}. The numbers of U.S. Representatives were CA

More information

a 2 x y 1 y SOL AII.1a

a 2 x y 1 y SOL AII.1a SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas

More information

Chapter 6. Exploring Data: Relationships

Chapter 6. Exploring Data: Relationships Chapter 6 Exploring Data: Relationships For All Practical Purposes: Effective Teaching A characteristic of an effective instructor is fairness and consistenc in grading and evaluating student performance.

More information

MATH 1710 College Algebra Final Exam Review

MATH 1710 College Algebra Final Exam Review MATH 7 College Algebra Final Eam Review MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. ) There were 80 people at a pla. The admission price was $

More information

Algebra 1 Midterm Name

Algebra 1 Midterm Name Algebra 1 Midterm 01-013 Name Stud Guide Date: Period: THIS REVIEW WILL BE COLLECTED JANUARY 4 th or Januar 7 th. One problem each page will be graded! You ma not turn this eam review in after the due

More information

4 The Cartesian Coordinate System- Pictures of Equations

4 The Cartesian Coordinate System- Pictures of Equations The Cartesian Coordinate Sstem- Pictures of Equations Concepts: The Cartesian Coordinate Sstem Graphs of Equations in Two Variables -intercepts and -intercepts Distance in Two Dimensions and the Pthagorean

More information

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions.

Algebra II Notes Unit Six: Polynomials Syllabus Objectives: 6.2 The student will simplify polynomial expressions. Algebra II Notes Unit Si: Polnomials Sllabus Objectives: 6. The student will simplif polnomial epressions. Review: Properties of Eponents (Allow students to come up with these on their own.) Let a and

More information

Review of Essential Skills and Knowledge

Review of Essential Skills and Knowledge Review of Essential Skills and Knowledge R Eponent Laws...50 R Epanding and Simplifing Polnomial Epressions...5 R 3 Factoring Polnomial Epressions...5 R Working with Rational Epressions...55 R 5 Slope

More information

Precalculus Honors - AP Calculus A Information and Summer Assignment

Precalculus Honors - AP Calculus A Information and Summer Assignment Precalculus Honors - AP Calculus A Information and Summer Assignment General Information: Competenc in Algebra and Trigonometr is absolutel essential. The calculator will not alwas be available for ou

More information

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #11 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

a 2 x y 1 x 1 y SOL AII.1a

a 2 x y 1 x 1 y SOL AII.1a SOL AII.a The student, given rational, radical, or polnomial epressions, will a) add, subtract, multipl, divide, and simplif rational algebraic epressions; Hints and Notes Rules for fractions: ) Alwas

More information

MATH GRADE 8 UNIT 4 LINEAR RELATIONSHIPS ANSWERS FOR EXERCISES. Copyright 2015 Pearson Education, Inc. 51

MATH GRADE 8 UNIT 4 LINEAR RELATIONSHIPS ANSWERS FOR EXERCISES. Copyright 2015 Pearson Education, Inc. 51 MATH GRADE 8 UNIT LINEAR RELATIONSHIPS FOR EXERCISES Copright Pearson Education, Inc. Grade 8 Unit : Linear Relationships LESSON : MODELING RUNNING SPEEDS 8.EE.. A Runner A 8.EE.. D sec 8.EE.. D. m/sec

More information

Mathematical Modeling

Mathematical Modeling Mathematical Modeling Sample Problem: The chart below gives the profit for a company for the years 1990 to 1999, where 0 corresponds to 1990 and the profit is in millions of dollars. Year 0 1 2 3 4 5 6

More information

SOLVING SYSTEMS OF EQUATIONS

SOLVING SYSTEMS OF EQUATIONS SOLVING SYSTEMS OF EQUATIONS 4.. 4..4 Students have been solving equations even before Algebra. Now the focus on what a solution means, both algebraicall and graphicall. B understanding the nature of solutions,

More information

LESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II

LESSON #28 - POWER FUNCTIONS COMMON CORE ALGEBRA II 1 LESSON #8 - POWER FUNCTIONS COMMON CORE ALGEBRA II Before we start to analze polnomials of degree higher than two (quadratics), we first will look at ver simple functions known as power functions. The

More information

OHS Algebra 2 Summer Packet

OHS Algebra 2 Summer Packet OHS Algebra 2 Summer Packet Good Luck to: Date Started: (please print student name here) Geometry Teacher s Name: Complete each of the following exercises in this formative assessment. To receive full

More information

6.1.1 How can I make predictions?

6.1.1 How can I make predictions? CCA Ch 6: Modeling Two-Variable Data Name: Team: 6.1.1 How can I make predictions? Line of Best Fit 6-1. a. Length of tube: Diameter of tube: Distance from the wall (in) Width of field of view (in) b.

More information

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II

LESSON #12 - FORMS OF A LINE COMMON CORE ALGEBRA II LESSON # - FORMS OF A LINE COMMON CORE ALGEBRA II Linear functions come in a variet of forms. The two shown below have been introduced in Common Core Algebra I and Common Core Geometr. TWO COMMON FORMS

More information

Functions. Introduction

Functions. Introduction Functions,00 P,000 00 0 970 97 980 98 990 99 000 00 00 Figure Standard and Poor s Inde with dividends reinvested (credit "bull": modification of work b Praitno Hadinata; credit "graph": modification of

More information

Algebra 2 Unit 2 Practice

Algebra 2 Unit 2 Practice Algebra Unit Practice LESSON 7-1 1. Consider a rectangle that has a perimeter of 80 cm. a. Write a function A(l) that represents the area of the rectangle with length l.. A rectangle has a perimeter of

More information

Essential Question How can you use a scatter plot and a line of fit to make conclusions about data?

Essential Question How can you use a scatter plot and a line of fit to make conclusions about data? . Scatter Plots and Lines of Fit Essential Question How can ou use a scatter plot and a line of fit to make conclusions about data? A scatter plot is a graph that shows the relationship between two data

More information

HSML Honors or AP Calculus Course Preparedness Test

HSML Honors or AP Calculus Course Preparedness Test HSML Honors or AP Calculus Course Preparedness Test High School Math Live wants parents to be well informed. We want our student to be placed in the appropriate course so that the will be successful and

More information

10.2 Graphing Exponential Functions

10.2 Graphing Exponential Functions Name Class Date 10. Graphing Eponential Functions Essential Question: How do ou graph an eponential function of the form f () = ab? Resource Locker Eplore Eploring Graphs of Eponential Functions Eponential

More information