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