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**Directions:**

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

**LABEL ALL YOUR ANSWERS APPROPRIATELY!!!**

**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

**showing all your work**

. When necessary, round your answer to the nearest ten thousandth. Circle your final answer.

**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?