Algebra 2
TEST REVIEW FOR EXAM #1 SPRING 2015
Example #1

Which expression shows the value of a $2500 investment after it has grown
by 4.5% per year for 12 years?

A) 2500 1.045
12

B) 2500 1.045
144

C) 2500 1.45

D) 2500 1.45
12
144
Example#2

A balloon with a small leak loses 0.5% of its volume each day. If it
originally contained 40 liters of gas, what is the volume of the gas after
one week?
A) 40 .05 7
B)
40 − 40 .005
C) 40 .95 7
D)
40 .995
7
7
Example#3

Which of the following functions is an example of exponential growth?
A) 𝑎(𝑥) = 1.5 0.85 𝑥
B)
C)
D)
b(x) = 4.07𝑥 1.3
c(x) = 0.5 2
𝑥
d(x) = log3 x4
Example#4
Which is the inverse of 𝑓 𝑥 = 2 − 4𝑥?
A) 𝑔 𝑥 =
𝑥+4
2
B) 𝑔 𝑥 =
𝑥−4
−2
C) 𝑔 𝑥 =
𝑥−2
−4
D) 𝑔 𝑥 =
𝑥+2
−4
Example#5

Which is the inverse of the following 𝑓 𝑥 =

A) 𝑔 𝑥 = 2𝑥 − 4

B) 𝑔 𝑥 = 2𝑥 + 4

C)𝑔 𝑥 = 4𝑥 − 2

D) 𝑔 𝑥 = 4𝑥 + 2
𝑥+4
2
?
Example#6

Which is the logarithmic form of 𝑥 4 = 5?

A) logx 4 = 5

B) log x4 = 5

C) log4 5 = x

D) logx 5 = 4
Example#7

Which is the logarithmic form of 43 = 64 ?

A) 𝑙𝑜𝑔4 3 = 64

B) log 4 64 = 3

C)𝑙𝑜𝑔3 4 = 64

D) 𝑙𝑜𝑔64 4 = 3
Example#8

Which is the logarithmic form of 53 = 125
A) 𝑙𝑜𝑔5 3 = 125
B) log 5 125 = 3
C)𝑙𝑜𝑔3 125 = 5
D) 𝑙𝑜𝑔125 5 = 3
Example#9

Which is the exponential form of log 2 32 = 5 ?

A)232 = 5

B) 325 = 2

C)25 = 32

D)52 = 32
Example#10

Express log 2 32 + log 2 4 as a single logarithmic

A) log 2 8

B) log 2 36

C)log 2 128

D)log 2 28
Example #11

Express log 2 32 − log 2 4 as a single logarithmic

A) log 2 8

B) log 2 36

C)log 2 128

D)log 2 28
Example#12

Simplify the following expression 2 log 5 5+ 3log 5 3

A) 2

B)3

C)4

D)5
Example#13

Solve

log 𝑥 + 1 + log 2 = 2

A)46

B)47

C)48

D)49
Example #14

Solve

4−𝑥 = 32

A)-1.5

B)-2

C)-2.5

D)-3
Example#15

Solve

log3 𝑥 4 = 8

A)9

B)10

C)11

D)12
Example#16


Solve
log 75x − log 3 = 1

A)0.2

B)0.3

C)0.4

D)0.5
Example#17

For f(x) = 𝑥 3 + 2, write the rule for each function and sketch its graph.

1. 𝑔 𝑥 = 𝑓 𝑥 + 1

Translate f(x) 1 unit __up____________.

g(x) =_𝑥 3 + 3____________________

2. g(x) = f(x - 3)

Translate f(x) 3 units _to the left _____________.

g(x) = __ 𝑥 − 3
3
+ 2______________
Example#18



Let f(x)= 2𝑥 4 − 6𝑥 2 + 4. Describe g(x) as a transformation of f(x) and write
the rule for g(x).
1. g(x) = 2f(x)
2. g(x) = f(2x)