34 questions

Worksheet 6 Name:

Problems 1-2. Determine if the function is exponential. If so then determine the growth/decay

factor.

1)

4

( ) 3h x x 2)

1

( ) 3

3

x

f x

Problems 3-6. Sketch the graph. Make sure to label at least three points and the horizontal

asymptote.

3) ( ) 3

x

f x 4)

1

( )

2

x

g x

5)

2

( ) 2 3

x

f x

6)

3

( ) 2 2

x

f x

Problems 7-10. Sketch the graph. Make sure to label at least three points and the vertical asymptote.

7)

3

( ) log ( )f x x 8)

2

( ) log (3 )g x x

9)

2

( ) log ( 3) 2f x x 10)

2

( ) log (1 ) 4f x x

Problems 11-16. Write the logarithm in exponential form.

11) log ( ) 3

b

x 12) ln(5) 8 2x 13) 5 log( ) 2 127x

14)

4

log ( 7) 8 2x 15)

9

2 log ( 2) 9x 16)

2

3log( 2) 1 13x

Problems 17-22. Write the exponential in logarithmic form.

17) 3 11

x

e 18)

5

1.3 x 19)

4

7

2

x

y

20)

9

2.3 7

x

21)

3

10 1

3

2

x

22)

3 5

7

x

e z

Problems 23-26. Simplify.

23)

3

log (9) 24)

700

7

log (49 ) 25) 2

1

2 log ( ) 3

4

26)

7

1

ln

e

Problems 27-30. Determine the domain and range of the function. Write in interval notation.

27)

1

( ) 2 2

x

f x

28) ( ) ln( 3) 4g x x

29)

1

( ) 3 4

x

f x

30)

2

( ) log ( 2) 3h x x

31) Find the amount after 3 years if $1000 is invested at an interest rate of 12% per year, compounded

continuously.

32) A sum of $1200 is invested at an interest rate of 7.5% per year. Find the amount in the account after 4

years if interest is compounded monthly.

Problem 33. Expand the logarithm. (2 points)

33)

3 7

5 2

log

9 ( 3)

x

x x

Problem 34. Combine. Write as a single logarithm. (2 points)

34)

1

ln(3) 5 ln( 3) ln( 1) 3ln( ) 5 ln( )

3

x x x x

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