Unit 4

An Introduction to Functions

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Functions
Essential Question: How can you represent and describe functions?

Modeling
Essential Question: Can functions describe real-world situations?

Ceteris Paribus
Essential Question: Loosely translated from Latin, ceteris paribus means "all other things held constant"  How can the analysis of functional relationships between two variables be useful when other variables impact the functional relationship, too?
 

FUNCTION
MACHINE

 


on x-y system
Graphing Calculator
Lesson/Objective Supplemental Lessons On-line Practice Homework
4-1  Using Graphs to Relate Two Quantities

Objective:  To represent mathematical relationships using graphs

Essential Understandings: 
Graphs can be used to visually represent the relationship between two variable quantities as they change.

Tables and Graphs can both show relationships between variables.
 


Video Tutors

Interpreting a graph that is related to events

Sketching a graph that is related to events


on x-y system


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-1: Due Mon Dec 10
1) Read pgs 234-236
2) pg 237-239 #1-3, 5-13,19,20

 

4-2  Patterns and Linear Functions

Objective:  To identify and represent patterns that describe linear functions  

Essential Understandings: 
The value of one variable may be uniquely determined by the value of another variable.  Such relationships may be represented using words, tables, equations, sets of ordered pairs, and graphs.

 


Video Tutors

Identifying independent and dependent quantities

Writing a rule from a table


self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-2: Due Wed Dec 12
Read section 4-2
pg 243-245 #2,3,5, 6-10 ALL, 11,19

Complete Tiling Garden Beds Lab and Analysis

4-3  Patterns and Non-Linear Functions

Objective:  To identify and represent patterns that describe nonlinear functions

Essential Understandings: 
Just like linear functions, nonlinear functions can be may be represented using words, tables, equations, set of ordered pairs, and graphs.

A nonlinear function is a function whose graph is not a line or part of a line.
 


Video Tutors

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-3: Due Fri Dec 14
pg 249-251
#1-4, 8-11, 21

hw#4-4: Due Fri Dec 14

pg 252  #1-11 All
pg 282-283 #6-12 Even
pg 257 #9-14 All

4-4  Graphing a Function Rule

Objective: To graph equations that represent functions

Essential Understandings: 
The set of all solutions of an equation form its graph

A graph may include solutions that do not appear in a table

A real world graph should show only points that make sense in the given situation.
 


Video Tutors

Making a table from a function rule

finding the  range of a function given the domain

Modeling a function using three views

discrete vs. continuous data

graphing a nonlinear function

Solve It!

Additional
PROBLEMS

Enrich!

 

QUIZ on 4-1 thru 4-4
NO QUIZ!! (See Test Date Below)

4-5  Writing a Function Rule

Objective: To write equations that represent functions

Essential Understandings: 
Many real-world functional relationships can be represented by equations. You can use an equation for find the solution of a given real-world problem.

 

Video Tutors

writing a function from words

finding the  range of a function given the domain

 

self-check quiz

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-5: Due Tues Dec 18
pg 266-67
#24-29 All & 31... watch out for functions whose dependent variable DECREASES as the independent variable INCREASES!
#37-51 Odd

You should also begin looking at/doing the Chapter Review in the textbook

4-6  Formalizing Relations and Functions

Objective: To determine whether a relation is a function. To find domain and range and use function notation

Essential Understandings: 
A function is a special type of relation where each value in the domain is paired with one value in the range.

The vertical line test shows whether a function is a relation.
 


Video Tutors

determining a reasonable domain and range for a situation

identifying a functions using a mapping diagram

identifying functions using the vertical line test

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-6 Due  Tues Dec 18

pg 271-273
#6-39 Mult of 3

 

 

 

 

4-7  Sequences and Functions

Objective: To identify and extend arithmetic sequences using function notation

Essential Understandings: 
Some sequences have function rules that can be used to find any term in the sequence

When the pattern in a sequence is identified, the sequence can be extended
 


Video Tutors

finding the common difference of an arithmetic function

finding the value of the nth term of an arithmetic function

Solve It!

Additional
PROBLEMS

Enrich!

hw#4-7 Due 
  pg 277-279
#13-23 Odd
#31-43 Odd
#49-53 Odd

Have you learned how to use the:

?

UNIT TEST REVIEW   UNIT 4 EXTRA PRACTICE

UNIT 1-4 CUMULATIVE REVIEW

hw#4-8 Due 
The Chapter Review and Chapter Test problems in the textbook are all FAIR GAME for the UNIT TEST... can you do them??
UNIT 4 TEST Sections 4-1 thru 4-7:
Thursday, Dec 20th