CHAPTER 4, FORM A
COLLEGE ALGEBRA
NAME
DATE
1. Consider the function defined by
( )
9f x x=+
.
a. What are the domain and range of f? 1a._______________________________
b. Write an equation for
( )
1
fx
−
. 1b._______________________________
c. What are the domain and the range of
1
f−
? 1c._______________________________
2. Match the equation with its correct graph:
4x
y−
=
2. _______________________________
(a) (b)
(c)
(d)
Graph the function.
4. Solve
31
25 125
xx-+
=
. 4._______________________________
( )
1
3
x
fx 
=

3.
5a. Write
3
6 216=
in logarithmic form. 5a._______________________________
5b. Write
4
log 1024 5=
in exponential form. 5b._______________________________
CHAPTER 4, FORM A
6. Use properties of logarithms to write the following 6._______________________________
as a sum, difference, or product of logarithms.
7
45
ln x
yz
Use a calculator to find approximations for each of the following logarithms. Express answers to three decimal
places.
7. ln 650 7._______________________________
8. ln q = 3.5 8._______________________________
9.
2
log 5
9._______________________________
10.
If ( ) x
f x a=
and f (3) = 125, find the following values of f (x).
a. f (0) 10. a._______________________________
b. f (–2) b._______________________________
11. What values of x cannot possibly be solutions of 11._______________________________
the following equation?
1og (3 1) 2
ax+=
Use properties of logarithms to solve each equation. Express answers to three decimal places.
12.
1og log( 6)xx=−
12._______________________________
13.
22
log ( 7) log 3xx+ + −
13._______________________________
14.
22
2log 3 log ( 2)xx= + −
14._______________________________
15.
ln(2 5) ln3 ln( 1)xx+ – = –
15._______________________________
16. Between what two consecutive integers must x be 16._______________________________
if 4 32?
x=
Explain why this is so.
17. The temperature of a liquid t minutes after being 17._______________________________
placed into an environment having constant
temperature
0
T
is given by
–.15
0
( ) 100 .
t
T t T e=+
How long, to the nearest minute, will it take a cup
of hot tea to cool to a temperature of 20° C in a
room at 15° C?
18. If $1,500 is invested at a rate of 2.5% per year 18._______________________________
compounded quarterly, what is the principal
after one year?
CHAPTER 4, FORM A
19. A radioactive substance is decaying so that the
number of grams present after t days is given by
the function
–0.015
( ) 2000 t
A t e=
a. Find the amount of the substance, to the nearest 19. a._______________________________
tenth of a gram, present after 60 days.
b. Find the half-life of the substance. b._______________________________
20. The population of a town is 1250 and increasing 20._______________________________
at a rate of 1.3% per year, while the number of
cats in the town is currently 200 and increasing at a rate of
9% per year. Assuming this trend continues, estimate
graphically when the cat population will exceed the human
population in this town.
CHAPTER 4, FORM A