Name: Period:
College Algebra: Ch4.1 – 4.4 Test
You must show all supporting work for all answers to receive credit. No Calculators.
For 1 - 5, choose the one alternative that best completes the statement or answers the question. Supporting work and/or reasoning must be provided to receive credit for your answer.
(+2 ea)

3 , what does 8
2 x equal?
1. _____
1. If 2
3 x
A.
1
9
B.
27
1
C.
27
D.
9
E.
None of these.
2. Where would the point (16, 2) for the parent function end up after being transformed according to f ( x )
 
3 log
4
 x

1


2 .
2. _____
A.
(-51, 0) B.
(17, 4)
3. Determine
 f  g
 
when f ( x )
 
C.
(-45, 4) D.
(-45, 0)
3 x

15 and g ( x )

2 x
2  x
A.
3 5 B.
15 C.

5 3 D.
-15
4.
Determine the Domain of the logarithmic function. H ( x )
 log
4 x x


3
2
A.


3 , 2

E.
None of these.
E.
None of these.
4. _____
3. _____
B.

 
,

3
 and

2 .
 

C.
[ 2 ,
 
) D.

 
,

3
 and

2 ,


E.
None of these.
5.
The volume of a hot air balloon as a function of radius, r , is given by V ( r )

4
3
 r
3
. Find the volume of the balloon as a function of time if the radius varies with time according to r ( t )

1
3 t
3
. 5. _____
A.
V ( t )

4
81
 t
9
B.
V ( t )

4
81
 t
6
C.
V ( t )

4
9
 t
9
D.
V ( t )

2
 t
9
E.
None of these.
D

6.
Given f ( x )

3 x

2
2 x

1 and g ( x )

2 x

3 x
, determine
 f  g
 
and its Domain.
7. Determine the inverse of f ( x )
 your answer for the inverse is correct.
4 x

1
3 x

2 and the Domain and Range of f
6.
_______________________
(+3)
D: _______________________
(+2)

1
( x ) . Verify algebraically that
7.
___ _____________________
(+3)
D: _______________________
(+1)
8.
Determine the equation of the transformation for the parent function
.
R: _______________________
(+1)
8.
___ ________________________
(+5)

Solve the following equations algebraically.
9. 27 x 
9 x
1
11. log
100

3
2 x

1
9

9 x

4
10. 2
6 
1

32 x
8
2
3 x

1
12. log
2
 x
2 
11 x

32


3
9.
_______________
(+5)
10.
_______________
(+5)
11.
_______________
(+5)
12.
_______________
(+5)

For 13 and 14, state final values of the key/ critical points, domain, range (both in interval notation), and asymptotes of the function. Sketch a graph
(+4)
on the axes, labeling all key information.
13. f ( x )

1

 
3 x

2
14. f ( x )

2

1
3 log
3
 x

2

13. Points: ______________
(+1)
______________
(+1)
______________
(+1)
Asymptote: __________________
(+1)
D: _________________________
(+1)
R: _________________________
(+1)
D:_______________________(1)
R:_______________________(1)
A:_______________________(1)
14. Points: ______________
(+1)
______________
(+1)
______________
(+1)
Asymptote: __________________
(+1)
D: _________________________
(+1)
R: _________________________
(+1)