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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