Grades 8-12 
Mathematics 
Algebra II 
Standard 24
Students solve problems involving functional
concepts such as composition, inverse, and
arithmetic operations on functions.

 

Resources
Lesson Plans
Assessments
Algebra 2  
An Integrated Approach,  Larson/Kanold/Stiff, 1995, 
D.C. Heath and Company 

Section References 

6.1 Relations and Functions 

6.2 Function Operations 

6.3 Inverse Functions 

6.4 Special Functions 

9.1 Operations with Polynomials 

10.2 Inverse and Joint Variation 

10.3 Multiplying and Dividing Rational Expressions 

10.5 Addition, Subtraction, and Complex Fractions 

Software 

Tangible Math:  
Algebra Animator,  
LOGAL Software, Inc. 
floppy mac/windows 

CA Exit Exam Web Site 

http:/www.chspe.com/ 
download.html 

Specific Textbook   
Web Sites    

http://www.glencoe.com/  
sec/math/prealg/mathnet/    

http://www.eduplace.com/  
links/    

http://www.eduplace.com/    

http://www.hmco.com/  
college/mathematics/  
index.html    

http://www.mcdougallittell  
.com/    

http://www.hmco.com/    

http://www.SRA-4KIDS.com/    

General Math   
Reference Sites    

http://www.learner.org/  
sami/view-category.php3  
?category=math    

http://www.score.k12.ca.us/    

http://henson.austin.apple  
.com/edres/curric.shtml    

http://school.discovery.com/  
schrockguide/index.html    

http://www.EDsOasis.org/    

http://www.math.com/    

http://www.nea.org/grants/  
free.html    

http://www.wcom.com/  
marcopolo/    

http://www.udel.edu/sine/    

http://dewey.chs.chico.k12  
.ca.us/math.html    

Free Stuff    

http://www.nea.org/  
grants/free.html    

State/National Math   
Ed Organizations    

http://www.nctm.org/    

http://www.cde.ca.gov/    

Calif. Dept. of Ed. Standards, Assessment, Ed. Reference.    

Calculator Reference Site    

http://www.ti.com/  
calc/docs/calchome.html  

Previously Published Data 

1.) Determine whether each pair of functions are inverse functions: 

f(x) = -2x + 3  

f(x) = x  

f(x) = x + 4 

g(x) = 2x - 3 

g(x) = -x  

g(x) = x - 4 

2.) For each pair of functions, f and g, find (f o g)(x) and (g o f)(x). 
f(x) = 2x - 1  
f(x) = x(x) + 2 
g(x) = 3x + 4  
g(x) = x - 3 
3.) If f = ((2,1), (-1,6), (3,2)) and g = ((2,2), (6,-1), (1,5)), express f o g and g o f, if they exist, as ordered pairs. 
4.) If f(x) = 3x - 3 and g(x) = 2x + 1, find (f + g)(x). If f(x) = x - 1, find f to the -1 (x). x + 1 
Previously Published Data 

1.) Describe composite functions in functional notation f(g(x)), and give at least two examples and their real world applications. 

2.) Explain how to determine the inverse of a function. Give an example with your explanation. 
3.) Express f o g and g o f, if they exist, as sets of ordered pairs: 

f = ((1,1), (0,3)) and  

g = ((1,0), (-3,1), (2,1)) 

f = ((3,8), (4,0), (6,3), (7,1)) and 

g = ((0,4), (8,6), (3,6), (-1,8)) 

4.) Name two functions f and g such that f(g(x)) = g(f(x)). 
5.) If f(0) = 4 and f(x + 1) = 3f(x) -2, find f(4).