Honors Algebra II
Linear-Quadratic Systems Extra Practice (Original is landscaped)
Solve each system using the substitution method.
1.
2.
3.
4.
7.1 – 7.4 Review
Honors Algebra II
Name
Math History
Complete the following exercises. Find the answers to the exercises in the boxes at the bottom of the
page. Place the letter from the box on the corresponding line with the number of the exercise. These
letters will then give the name of the mathematician that is credited with introducing the radical sign.
1. Rewrite
4. Simplify (32/5  41/3)3.
in rational exponent notation.
 35
5. Simplify  5
6
2. Rewrite 85/4 in radical notation.
3. Evaluate



1 / 2
8
6. Write 4 x in simplest form.
y3
In Exercises 7-14, f(x) = x2 + 1. g(x) = x 3, h(x) = x3/2, and m(x) = 2x + 1
7. Find f(x) + g(x).
12. Find f(g(x)).
8. Find g(x)  f(x).
13. Find g(f(x)).
9. Find g(x)  h(x).
14. Find g1(x).
10. Find h(x)  h(x).
15. Find
11. Find h(f(x)).
16. Find
D
2
x + x 4
T
 8
R
71/9
S
or 25/2
4
A
5/2
1
 
2
x
2
E
5
H
4
y
y
 8
5
.
.
R
9
4
3
F
4
6/5
O
-17
F
(x2 + 1)3/2
M
x3 + 1
B
3x
Y
4
5
O
x  6x + 10
P
126/5
U
x +x2
W
79
F
x5/2  3x3/2
F
2
L
x+3
c
x2  2
G
36
I
x3
2
2
_____ _____ _____ _____ _____ _____ _____ _____ _____
13.
6.
1.
10.
5.
2.
16.
9.
4.
_____ _____ _____ _____ _____ _____ _____
3.
7.
8.
12.
14. 11.
15.
Honors Algebra II
Unit 5 Part I Study Guide (7.1 – 7.4)
(7-1 & 7-2) Rational Exponents and Radicals
 Be able to use the rules of exponents.
 Be able to solve equations involving exponents.
 Be able to add, subtract, multiply and divide radical expressions with and
without variables.
 Be able to add, subtract, multiply and divide radical expressions involving
rational exponents with and without variables.
(7-3) Composition of Functions:
 Be able to perform operations and composition of functions involving powers,
roots, and radicals.
 Be able to state the domain.
 Be able to evaluate composition of functions.
(7-4) Inverse Functions:





Be able to find the inverse of an equation.
Be able to match inverse graphs.
Be able to use the horizontal line test.
Be able to verify that two functions are inverses of each other.
Be able to write an inverse model and use it to make predictions.
Example: A model for a telephone bill is T  005
. m  29.95 , where T is the total bill, and
m is the number of minutes used.
a. Find the inverse model.
b. If the total bill is $54.15, how many minutes were used?
Honors Algebra II
Unit 5 Part II Study Guide (7.5 & 7.6)
(7-5) Graphing and Describing Radical Functions
 Know the characteristics about cubic, cube root and square root functions.
 Know the relationship between cubic and cube root functions.
 Be able to describe a square root and a cube root function from its parent function using a, h, and k.
 Be able to find the domain and range of radical functions.
 Be able to graph a square root and cube root function using a table.
Example #1 Describe the transformation of y  
domain and range.
2
x  3  4 from its parent function and then state the
3
Example #2
and range.
Describe the transformation of
from its parent function and then state the domain
Example #3
Create a table and graph each function.
a.
b.
(7-6) Radical Equations:
 Be able to solve equations involving rational exponents and radicals.
 Be able to check for extraneous solutions.
 Be able to solve real life problems involving radicals or rational exponents.
Example #4 Solve each equation.
a. 3 2 x  4  12
b.
d.
e.
Example #5:
3
x2  9  3
c.
f.
Unit 6 Review
Name
Date
Class
Complete the table.
1.
2.
 2
y 
 5
Growth or Decay
3.
 x 2
y3
x
1
y
y -intercept
Asymptote
Domain
Range
Graph/Translation
Complete the table.
4.
y  log1 3 x  1
5.
y  log4 ( x  2)  3
Moves up or down to the
right
Vertical Asymptote
Domain
Range
Translation of
f ( x)  logb x
Simplify each expression.
2
6. ( 3e)( e )
7.
e4  3

e3 e
8. ln e 4x
9. log 4 64
1 x
e
2
11.
10. log 125 5
12. log3 27
13. log2 0.5
Evaluate
14.
15.
16.
Find the inverse of the function.


18. y  ln x  2
17. y  log 6 x
y  a 1  r 
t
y  a 1  r 
t
 r
A  P 1  
 n
19.
nt
A  Pert
20. You deposit $5000 in an account that pays 6.5% annual interest. Compare the balance after five
years compounding monthly and continuously. Which is the better investment? Explain your answer.
21. The value of a new car purchased for $20,000 decreases by 10% per year. Write an exponential
decay model for value of the car. Use the model to estimate the value of after three years.
Algebra 2 Honors
Unit 7 (9.2, 9.4, & 9.5) Review
Name
Describe and sketch the graph of each rational function. Label the asymptotes on the graph.
3x  2
2x  1
1. y 
2.
VA:
VA:
HA:
HA
Domain:
Domain:
Range:
Range:
3. y 
3
2
x3
4.
VA:
VA:
HA:
HA
Domain:
Domain:
Range:
Range:
Simplify each expression.
5.
7.
6.
21x10 y 5 x 3

5x 2
35 y 4
8.
9.
10.
11.
12.
13.
3x
3x  6
 2
2x  3 2x  x  6
14.
15.
2x  1
1

x x2 x2
16.
2
2 x 3  12 x 2
8 x 3  24 x 2

x 2  4 x  12 x 2  9 x  18