Algebra worksheet
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