Chapter 2 Overview 2 Functions, Equations, and...
2
S O L V E I T ! O I T V O C A B U L A R Y O C O A V I D E O V I D E O O N L I N E H O M E W O R K E E V O C A B U L A R Y S O L V E I T ! A C T I V I T I E S D Y N A M I C M E W O M E W O K M E W O W R R K K K F O R S C H O O L M a t h X L ® N L I I Your place to get all things digital Download videos connecting math to your world. Math definitions in English and Spanish The online Solve It will get you in gear for each lesson. Interactive! Vary numbers, graphs, and figures to explore math concepts. Online access to stepped-out problems aligned to Common Core Get and view your assignments online. Extra practice and review online You can use functions to model all kinds of real-world situations. A function can model something as simple as a line between two points or as complex as the curves of a roller coaster. You will learn how to work with functions in this chapter. Functions, Equations, and Graphs CHAPTER 2 Vocabulary English/Spanish Vocabulary Audio Online: English Spanish correlation, p. 92 correlación direct variation, p. 68 variación directa domain, p. 61 dominio function, p. 62 función linear equation, p. 75 ecuación lineal range, p. 61 rango relation, p. 60 relación slope, p. 74 pendiente V V I I D D E E O O V O V C O A B U L A A R Y R S O L V L E I I T T ! ! O I T C T I V I T I E A A A A A A A A C A T C C I E E E S S S S S S S S S S S S S S S S E D D D Y Y Y D D D N Y Y A M M I I I I C C our place to get l things digital deos ath . ons d wi get or , gures ath Online access o stepped-out problems aligne ed o Common Cor re You can us You s of r kinds function c f simple as or as comp roller coas work with Voca English/Span English correlation p9 DOMAINS • Interpreting Functions • Building Functions • Creating Equations 58 Chapter 2 Chapter 2 Overview Use these online assets to engage your students. These include support for the Solve It and step-by-step solutions for Problems. Show the student-produced video demonstrating relevant and engaging applications of the new concepts in the chapter. Find online definitions for new terms in English and Spanish. Start each lesson with an attention- getting Problem. View the Problem online with helpful hints. Chapter 2 Overview UNDERSTANDING BY DESIGN Chapter 2 expands on students’ understandings and skills related to functions, equations, and graphs. In this chapter, students will develop the answers to the Essential Questions posed on the opposite page as they learn the concepts and skills bulleted below. BIG idea Equivalence ESSENTIAL QUESTION Does it matter which form of a linear equation you use? • Students will identify different forms of linear equations. • Students will determine which form of a linear equation is most easily found with the given information. • Students will convert between various forms of linear equations. BIG idea Function ESSENTIAL QUESTION How do you use transformations to help graph absolute value functions? • Students will identify the different kinds of transformations. • Students will determine whether a transformation changes the location or shape of a graph or both. BIG idea Modeling ESSENTIAL QUESTION How can you model data with a linear function? • Students will make a scatter plot of linear data. • Students will determine the correlation of linear data. • Students will use linear regression to find the line of best fit of linear data with a graphing calculator. • Students will use the correlation coefficient to analyze linear data with a graphing calculator. Content Standards Following are the standards covered in this chapter. Modeling standards are indicated by a star symbol (★). CONCEPTUAL CATEGORY Functions Domain Interpreting Functions F.IF Cluster Interpret functions that arise in applications in terms of the context. (Standards F.IF.4★, F.IF.6★) LESSON 2-5 Cluster Analyze functions using different representations. (Standards F.IF.7★, F.IF.8★, F.IF.9★) LESSONS 2-4, 2-7 Domain Building Functions F.BF Cluster Build a function that models a relationship between two quantities. (Standard F.BF.3) LESSONS 2-6, 2-7
Transcript of Chapter 2 Overview 2 Functions, Equations, and...
S
OLVE IT!O IT
VOCA
BULARYOCO
A
VIDEO
0057_hsm11a2se_cc_02co.indd 59 3/28/11 4:25:28 PM
VIDEO
ONLINE
HO
M E W ORK
EE
VOCA
BULARY
S
OLVE IT!
AC T I V I T I E
S
DYNAMIC
M E W OM E W O
K
M E W OW
RRKKK
FO
R S C H OOL
MathXL ®
NLII
Your place to get all things digital
Download videos connecting math to your world.
Math definitions in English and Spanish
The online Solve It will getyou in gear foreach lesson.
Interactive! Vary numbers, graphs, and figures to explore math concepts.
Online accessto stepped-outproblems aligned to Common Core
Get and view your assignments online.
Extra practice and review online
You can use functions to model all kinds of real-world situations. A function can model something as simple as a line between two points or as complex as the curves of a roller coaster. You will learn how to work with functions in this chapter.
Functions, Equations, and Graphs
CHAPTER
2
VocabularyEnglish/Spanish Vocabulary Audio Online:
English Spanish
correlation, p. 92 correlación
direct variation, p. 68 variación directa
domain, p. 61 dominio
function, p. 62 función
linear equation, p. 75 ecuación lineal
range, p. 61 rango
relation, p. 60 relación
slope, p. 74 pendiente
VVIIDDEEOO
VOVCO
ABULAARYR
SOLVL E IITT!!O IT
C T I V I T I E
AAAAAAAAC
A
TCC
I EEESSSSSSSSSSSSSSSSEE
DDDYYYDDD
NYY AMMIIIICC
our place to getl things digital
deosath .
onsd
wigetor
,gures
ath
Online accesso stepped-out
problems aligneed o Common Corre
You can usYou s of rkinds
function cfsimple as or as comproller coaswork with
VocaEnglish/Span
English g
correlation p 9
DOMAINS• Interpreting Functions• Building Functions• Creating Equations
0057_hsm11a2se_cc_02co.indd 58 3/28/11 4:24:56 PM
58 Chapter 2
Chapter 2 OverviewUse these online assets to engage your students. These include support for the Solve It and step-by-step solutions for Problems.
Show the student-produced video demonstrating relevant and engaging applications of the new concepts in the chapter.
Find online definitions for new terms in English and Spanish.
Start each lesson with an attention-getting Problem. View the Problem online with helpful hints.
Chapter 2 OverviewUNDERSTANDING BY DESIGNChapter 2 expands on students’ understandings and skills related to functions, equations, and graphs. In this chapter, students will develop the answers to the Essential Questions posed on the opposite page as they learn the concepts and skills bulleted below.
BIG idea EquivalenceESSENTIAL QUESTION Does it matter which form of a linear equation you use?• Students will identify different forms of linear
equations.• Students will determine which form of a linear
equation is most easily found with the given information.
• Students will convert between various forms of linear equations.
BIG idea FunctionESSENTIAL QUESTION How do you use transformations to help graph absolute value functions?• Students will identify the different kinds of
transformations.• Students will determine whether a transformation
changes the location or shape of a graph or both.
BIG idea ModelingESSENTIAL QUESTION How can you model data with a linear function?• Students will make a scatter plot of linear data.• Students will determine the correlation of linear
data.• Students will use linear regression to find the
line of best fit of linear data with a graphing calculator.
• Students will use the correlation coefficient to analyze linear data with a graphing calculator.
Content StandardsFollowing are the standards covered in this chapter. Modeling standards are indicated by a star symbol (★).
CONCEPTUAL CATEGORY FunctionsDomain Interpreting Functions F.IF
Cluster Interpret functions that arise in applications in terms of the context. (Standards F.IF.4★, F.IF.6★)LESSON 2-5Cluster Analyze functions using different representations. (Standards F.IF.7★, F.IF.8★, F.IF.9★)LESSONS 2-4, 2-7
Domain Building Functions F.BFCluster Build a function that models a relationship between two quantities. (Standard F.BF.3) LESSONS 2-6, 2-7
0057_hsm11a2te_cc_02co.indd 580057_hsm11a2te_cc_02co.indd 58 5/9/11 4:52:28 PM5/9/11 4:52:28 PM
creo
AC T I V I T I E
SAAAAAAACCCCCC
AA
TTTTTCC
II V I TTT IIIII EEEEEEESSSSSS
DYNAMIC
ONLINE
HO
M E W ORK
O
HO
ONLINE
HO
H
M E WW OOW
RRKK
FO
R S C H OOL
MathXL ®
Chapter 2 Functions, Equations, and Graphs 59
1 EquivalenceEssential Question Does it matter which form of a linear equation you use?
2 FunctionEssential Question How do you use transformations to help graph absolute value functions?
3. ModelingEssential Question How can you model data with a linear function?
Chapter Preview2-1 Relations and Functions2-2 Direct Variation2-3 Linear Functions and
Slope-Intercept Form2-4 More About Linear Equations2-5 Using Linear Models2-6 Families of Functions2-7 Absolute Value Functions and Graphs2-8 Two-Variable Inequalities
0057_hsm11a2se_cc_02co.indd 59 3/28/11 4:25:28 PM0057_hsm11a2se_cc_02co.indd 58 3/28/11 4:24:56 PM
Functions, Equations, and Graphs 59
My Math VideoUse this photo to introduce the connection between a graph and the function that models the graph. This chapter defines and explores linear and absolute value functions and how to model data with a linear function.
ERROR PREVENTIONThis activity may be confusing if students sketch graphs that are not functions. This may happen if the roller coaster dips backwards.
EXTENSIONAsk students to sketch another graph modeling a different situation.
Increase students’ depth of knowledge with interactive online activities.
Show Problems from each lesson solved step by step. Instant replay allows students to go at their own pace when studying online.
Assign homework to individual students or to an entire class.
Prepare students for the Mid-Chapter Quiz and Chapter Test with online practice and review.
Q Picture a roller coaster. Geometrically, how is it shaped? [Sample: curves going up and down]
Q Many roller coasters follow a complex, three-dimensional path, while some curve up and down above and below a straight path. Sketch a roller coaster curving above and below a horizontal path on a coordinate grid. What does the sketch look like? [Sample: A graph of a curve that starts at the origin curves up and down and eventually reaches the x-axis again.]
Q How do the y-values change with respect to x-values along your graph? Look at small sections. For example, for the first section, the y-values increase as the x-values increase. What do you observe? [The x-values are always increasing. As the roller coaster goes up, the y-values increase, and as the roller coaster goes down, the y-values decrease.]
Content Standards (cont’)
CONCEPTUAL CATEGORY AlgebraDomain Creating Equations A.CED
Cluster Create equations that describe numbers or relationships. (Standard A.CED.2★) LESSONS 2-2, 2-3, 2-4, 2-5, 2-8
0057_hsm11a2te_cc_02co.indd 590057_hsm11a2te_cc_02co.indd 59 5/9/11 4:52:57 PM5/9/11 4:52:57 PM
creo
