CHAPTER 4, FORM B
COLLEGE ALGEBRA
NAME
DATE
1. Consider the function defined by
( )
4f x x=-
.
a. What are the domain and range of f? 1a._______________________________
b. Find the rule 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
32
3 27
xx+=
. 4._______________________________
–1
1
2
x
y
+

=

3.
5a. Write
4.1
3a=
in logarithmic form. 5a.
_______________________________
5b. Write
8
1
log 2b=
in exponential form. 5b.
_______________________________
CHAPTER 4, FORM B
6. Use properties of logarithms to write the following 6._______________________________
as a sum, difference, or product of logarithms.
2
3
log yz
x
Use a calculator to find approximations for each of the following logarithms. Express answers to three decimal
places.
7.
ln 248
7._______________________________
8.
ln 3.5q=
8._______________________________
9.
2
log 7
9._______________________________
10.
If ( ) and (4) 81,
x
f x a f==
find the following values of f (x).
a. f (5) 10. a._______________________________
b. f (–1) b._______________________________
11. What values of x cannot possibly be solutions of 11._______________________________
the following equation?
log (4 –1) –2
ax=
Use properties of logarithms to solve each equation. Express answers to three decimal places.
12.
4
log ( – 8) 3r=
12._______________________________
13.
33
2log 3log 5x=
13._______________________________
14.
1
log 25 2
a=
14._______________________________
15.
4 4 4
log ( 4) – log ( – 4) log 3xx+=
15._______________________________
16. Between what two consecutive integers must x be 16._______________________________
if 6 37?
x=
Explain why this is so. _______________________________
17. The number of bacteria in a certain culture is given
by the function
.05
( ) 300,000 ,
t
B t e=
where t is the time in hours after the beginning of
the experiment.
a. How many bacteria will be present after 48 hr? 17. a._______________________________
b. How long, to the nearest tenth of an hour, b._______________________________
will it take the number of bacteria in the culture
to double?
CHAPTER 4, FORM B
18. The temperature of a liquid t minutes after being 18._______________________________
placed into an environment having constant
temperature
0
T
is given by
–.2
0
( ) 100 .
t
T t T e=+
How long, to the nearest minute, will it take a bowl
of hot soup to cool to a temperature of 27°C in a room
at 20°C?
19. How many years, to the nearest tenth, will be needed 19._______________________________
for $2050 to increase to $3000 at 2.2% compounded monthly?
20. The population of a town is 2300 and increasing at a rate 20._______________________________
of 1.2% per year, while the number of dogs in the town is
currently 625 and increasing at a rate of 9% per year.
Assuming this trend continues, estimate graphically
when the dog population will exceed the human population
in this town.
CHAPTER 4, FORM B