# Chapter 8 Test Review ... Show all your work for full credit. ...

Chapter 8 Test Review Name___________________

Show all your work for full credit. Date___________________

For questions 1-8, let f ( x )

 x

2  x

3 and g ( x )

 x

5 . Perform each function operation.

1) f ( x )

 g ( x ) 2) ( f

 g )( x ) 3) f ( x )

 g ( x ) 4) g ( x ) f ( x )

5) (f+g)(x) 6) f(x) - g(x) 7) ( f

 g )( x ) 8)

 f g

 ( x )

9) The population of Fort Collins is currently estimated at 140,000. Write a function that models the population if it grows at 8% per year. Find the population in 10 years.

Write a function that models the population if it falls 5% per year. Find this population in 5 years.

For 10 and 11, f ( x )

2 x

2 and g ( x )

 x

2  x

2 . Find:

10) g  f ( 1 ) 11) f(g(-2))

For the function f(x) = -3x + 9,

12) Graph f(x) 13) Find its inverse, f

1 14) Graph f

1

For 15 and 16, identify whether the function represents exponential growth or exponential decay x

15) .

62 ( 1 .

23 ) x 16) 75

1

3

17) Graph this function. Clearly label at least 3 points. y

2 ( 5 ) x

18) For the following function, identify the parent function and what transformations you would make to the parent function. y

 

4 x

2 

3

What is the horizontal asymptote of the transformed function?

19) If you invest \$1000 in a continuously compounded account at an interest rate of 9%, how much will you have after 5 years?

Write these equations in logarithmic form

20) 3

4 

81 21) 5

3 

125

Evaluate each logarithm

22) log 27

3

23) log 1

5

24) log 10

25) Graph this logarithmic function. Clearly label at least 3 points. y

 log

3

( x

2 )

Write each logarithmic function as a single logarithm.

26) 3 log 5 + log 5 27) log

5

2 a

4 log

5

3 b 28) 4 ln 2

2 ln y

Expand these logarithms. a

2

29) log 30) log b

3 xy

2 z

Use the properties of logarithms to evaluate each expression.

31) 5 log

8

2

 log

8

2 32) log

6

72

 log

6

2

Solve each equation. Round to the nearest hundredth.

33) log 5 x

2 34) log( 5 x

5 )

2 35) ln x

 ln 3

5

36) 10

2 x 

40 37) 6

3 x 

20 38) ln( 2 x )

1

39) log x

 log 3

5

Use the change of base formula to rewrite each expression using common logarithms.

40) log 10

5

41) log 5

3