Review 2nd Semester
Algebra 2 A
Unit 5: Transformation. No Calc.
Write the parent function for each graph.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13. What causes the entire graph of f  x   a b  x  h   k to be stretch horizontally?
2
2
14. If I change f  x   2  x  5  to f  x   2x   5 , how does the graph change?
15. The graph of f  x   x has been flipped vertically and moved 6 units down. What’s the new equation?
16. If f(x) contains the point  4, 0  , what would the corresponding coordinates be in f 2x  6   3 ?
Graph plotting the necessary points. State the domain and range.
17. f  x   2 x  4
3
18. f  x     x  3  2
19. f  x   2x  4  3
Write the equation for the graph in the form y  a f  x  h   k . Note: there is no b.
20.
21.
Unit 6: Trigonometry Functions. No Calc.
Graph from 360 to 360 or 2 to 2 .


22. y  3sin  x    1
3

1 
24. y  2tan  x   2 (use radians)
2 
23. y  2cos  2x  90 
State the phase & vertical shift, amplitude, period, domain, and range. Then write the trig function.
25. Write a positive sin and cos for this one.
26.
Unit 7: Composite and Inverse Functions.
Use the relations to answer the following questions.
f  2,7  , 3,5  ,  6,5 
27. Are f and g functions?
28. State the domains g
30. Evaluate f  g  2
31. Evaluate f
g  2, 1  ,  4, 0  ,  4,3 ,  6,2 
29. Find f 1
g   6
Let f  x   3x  1 and g  x    x 2  3x  2 . Find the following.
32.
f  g  2
33.
f g  x 
34.
Use the graph to find the following.
38.
f  g  5
39.
f g   0
40.
f
g   4 
f
g   2
f x 
g x 
35.
g
f  x 
Find f  g  x   and g f  x   .
Find the inverse of the function.
Is f  x  inverse of g  x  ?
Is the inverse also a function?
41. f  x  
3x  4
5
2
42. f  x    x  3 , g  x   x  9
Graph the inverse of the given graph. Is the inverse a function.
43.
44.
45. What ordered pair (coordinate)
corresponds to f  4   2 ?
46. f  x   3x 7  5x 3 .
Find f f 1  32  .
Unit 8: Rational Exponents. No Calc.
Simplify.
47.
Simplify in scientific notation.

3x 4 y 5 2x 2 y

3
48.
 2x y

3 4
 x y
2
1



4
49.

3  10 
 4  10 
2

5  104  6  10 
50.
6
Simplify in radical form without a calculator. Put absolute value where necessary.
1
x y
51.
6
54.
 4a 
13
52.
20
1
3 4
5
a2
55.
 56 2
 x 


53.
3
3
56.
3
5
 27 
 4 
 x 
6

2
3
16x 8
Solve. Make sure you check for extraneous solutions.
57.
2  3x  4  4  7
1
58.
2
1
3x 3  x 3  10
Unit 9: Logarithmic Functions.
Write in exponential form.
Write in Logarithmic form.
Simplify each expression. (NC)
59. 3  log4 x
60. 5x  80
61. ln e k
62. 10log 4x
Expand as much as possible. Where possible,
Evaluate.
Condense to a single log whose leading coefficient
is 1. Where possible, evaluate. (NC)
 x 2y 
63. log2 

 32 
1
65. 2 log3  2log x   log 4
2
64. ln 3
x
2
e
Solve.
67. 9x 2 
 3
3x
69. 2log3  x  1   log3 4  2
68. 32x 1  375
70. log4 (4x  16)  log4 (2x  1)  log4 (x  4)
66.
log16
log2
nt
 r
Round all answers to the nearest hundredth. Formulas to use: A  P  1  
 n
A  Pe rt
71. How long will it take $12500 to grow to $30000 at 6.5% interest compounded continuously?
72. You put in $2500 into an account. If you want it to double in 8 years, what yearly interest rate should it be if
it was compounded monthly?
Unit 10: Piecewise functions.
Plot new origin with an open circle and draw the asymptote. Plot at least 5 points on the graph. Sketch the
graph. State the domain and the range. (NC)
73. f  x   
x 2
1
2

2
74. f  x   log2 ( x  3)  2
75. f  x   3  2x   1
Use the given information to write the equation for the graph in the forms:
b x h 
y a2
k
76.

y  a b  x  h    k
77.
78.
Graph the Piecewise Functions.
79.

y  a log2 b  x  h   k

3x  17 if x  4
2

h  x     x  1   6 if  4  x  2
 1
22 x 2  4 if x  2

b  1
h 3
Write the piecewise function for the graph and complete the graph analysis chart.
80.
Int of Inc
Int of Dec
minimums
maximums
Domain
Range
x-int
y-int
Asymptotes
Avg rate of Chge over  4,2 
Unit 11: Sequences & Series.
81.
a1  7 and an  29  an 1  . Find the first four terms of the sequence.
Indicate whether the following represents arithmetic sequence, geometric sequence, or neither.
82.
2, 5, 10, 17, 26 …
83.
an  3n
84.
Give the equation for the general nth term of each sequence. Simplify the equation.
85.
50, 30, 18, 10.8, 6.48...
86. common difference = –6, 29th term = 17
87. In an arithmetic sequence, a26  3 and a30  17 . What is a1 ?
Give the sum of each series.
88.
400 + 394 + 388 + … + (−26)
89.
8
 2  3
n
n 1
Does the infinite geometric series converge? If so, give the sum. If not, write “does not exist”.
90.
10 + 15 + 22.5 + 33.75…
n
91.
 2
6  

n 1  3 
93.
3 − 15 + 75 − … + 46,875

Write each series using sigma notation.
92. 25 + 29 + 33 + … + 113
94. What is the value of k in the geometric sequence?
9, k, 4,…
95. Mrs. Sigma earned $40,000 during her first year as a nurse. She received an 8% raise every year.
a. Write an equation for her salary of her nth year on the job.
b. What was her salary on her 10th year on the job?
c. What is the total amount she had earned in 10 years?
Unit 12: Probability and Statistics.
96. A zip code has 5 digits. The first digit can not be 0 or 1. The middle digit must be odd. How many possible zip
codes are there?
97. How many different ways can you choose a pitcher, catcher, in-fielder, and an out-fielder from a team of 9
players?
98. From a club of 15 members, how many ways can a group of 4 be selected?
99. There are 8 cars, 6 boats, and 10 motorcycles. If I pick one at random, what are the probability and the odds
that it will be a car?
100. The odds of you becoming a teacher is 5:13. What is the probability that you won’t become a teacher?
#101-103. There are 12 books, 7 newspapers, and 8 magazines. If you pick 6 at random,
101. What is the probability that you’ll have 4 books and 2 newspapers?
102. What is the probability that you’ll have at least 4 books?
103. What is the probability that you’ll have at least one book?
104. You randomly pick a card from a standard 52-deck card. What is the probability that you’ll get a number card
or a diamond card?
105. There are 7 doctors, 11 engineers, and 8 lawyers. If you randomly select three people, what is the probability
that the first person will be a doctor and the next two will be a lawyer?
106. You guess at all 9 questions on a multiple choice test. Each question has 3 choices. What is the probability
that you get exactly 5 correct?
107. In a lottery game, a player picks six numbers from 1 to 23. If the player matches all six numbers, they win
30,000 dollars. Each ticket cost $2. Find the expected value of this game if you buy one ticket.
Determine whether the graph is a function. State the
domain and the range. State the indicated value.
36.
37.
f 1  ________
f  x   3. x  _____