# Algebra 2 Essentials: Exam #6 Study Guide

### Name:________________________________Period:_____ Score:__________/100

Directions:

Graph each function, identify the domain and range, find its inverse, identify its domain and range, and graph it.

1)

f

(

x

)

2

x

6

-10 -5

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

5 10

2)

g(x)

3 x

-10 -5

12

10

8

6

4

2

-2

5 10

-4

-10

-12

-6

-8

3)

-10

h

(

x

)

(

x

4)

2

3

-5

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

5 10

4)

w

(

x

)

x

2

1

-10 -5

12

10

8

6

4

2

-2

-4

-6

-8

-10

-12

5 10

5)

State if the following represents a 1-1 function or not.

(A) y

1

2

(D) y

 x

3

3

(B) y

(E) x

 

(C) y

(F)

2

3

Directions:

Rewrite each exponential equation as a logarithmic equation.

6)

4

3

64

7)

10

2.57

x

Directions:

Rewrite each logaritmic equation as an exponential equation.

9)

log 125

5

3

10)

log

k m

w

8)

3

x

5

Directions: Rewrite

each logarithmic expression in base ten using the change of base formula.

When possible,

evaluate

the expression. SHOW ALL YOUR WORK.

11)

log

3

15

12)

log

3

w

13)

log

4

512

Directions:

Expand each logarithm.

14)

log

5

3

2m x

15)

log

7

6x

3 n

5

Directions:

Write each logarithmic expression as a single logarithm.

16)

1

2 log

9

m

3log

9

w

17)

4 log

x

5 log

k

1

3 log

w

18)

Directions:

Use the properties of logs to find the approximations of the following, given log 2 and log 5

0.7

0.3

19)

log 20

20)

log 0.4

21)

log 25

25)

log

7

4

x

23

6

18

28)

Directions:

Solve for x

22)

2 ln

x

 ln

e

5

15

23)

log

5

125

x

11

47

24)

log

16

4

x

5

16

10

5

x

9

75

26)

2

3

x

5

16

11

29)

2ln

x

3ln2

5

27)

5

e x

7

27

30)

4

x

7

25

31)

log

2

.03125

x

32)

e

4

x

7

507

34)

 

 log2

3

35)

37

4

x

1

1253

37)

log

2

2

x

2

 log

2

x

1

9

33)

2

x

3

36)

9

9

11

Directions:

Solve each problem showing all your work.

38)

Henry invested \$1200 in a 6 year CD at a 5.25% interest rate. The interest is compounded monthly. How much money will Henry have when his CD matures?

39)

Katherine invests \$1000 in a 5 year CD that compounds interest continuously. She was thrilled to lock in at a 5.73% interest rate. How much money will Katherine have when her CD matures?

40)

How long will you have to invest \$500 if you earn 3.74% compounded continuously and you want to double your money?