Name:
Period:
MU
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)
1. If 32 x  3 , what does 94 x equal?
1. _____
A. 1
16
2.
C.
B. 16
1
81
D. 27
Where would the point (16, 2) for the parent function end up after being transformed according
2. _____
to f ( x)  2 log 4 x  5  3 .
A. (21, -1)
3.
B. (21, 0)
Determine
 f  g  2 when
C. (11, -1)
D. (11, 2)
3. _____
C.  2 15
D.
102
 x5 

 2x  3 
Determine the Domain of the logarithmic function. H ( x)  log 7 
A.  5, 3 



2
E. None of these.
f ( x)   2 x  82 and g ( x)  3x 2  1
B. 233
A. 15 3
4.
E. None of these.
3

B.  ,5 and  , 
2

3

C.  , 
2

3

D.  ,5 and  , 
2

E. None of these.
4. _____
E. None of these.
1 2
r h . Find the volume of the balloon as a
3
3 2
1 3
5. _____
function of time if the radius and height varies with time according to r (t )  t and h(t )  t .
4
2
5.
A.
The volume of a cone shaped balloon is given by V (r ) 
V (t ) 
3 7
t
32
B. V (t ) 
1 7
t
8
C. V (t ) 
32 7
t
3
7
D. V (t )  2t
E. None of these.
6. Given f ( x) 
2x  5
x3
and g ( x) 
, determine (a) g  f x and its Domain.
3x  1
x3
6. _______________________ (+3)
D: _______________________ (+2)
4x  1
and the Domain and Range of f
2x  3
your answer for f 1 ( x) is the correct inverse.
7. Determine the inverse of f ( x) 
1
( x) . Verify algebraically that
7. ________________________ (+3)
D: _______________________ (+1)
R: _______________________ (+1)
8. Determine the equation of the transformed graph.
8. ___________________________ (+5)
Solve the following equations algebraically.
12
9. 2
4
x2
 32
2x
 1  12
11. log 2   
x2
 32  5
 1  x
 4
 32 
6
10. 4 
2 3 x 2

9. _______________ (+5)
10. _______________ (+5)

12. log 5 x 2  3x  10  2
11. _______________ (+5)
12. _______________ (+5)
For 13 and 14, state final values of the parent key/ critical points, domain, range (interval notation), and
asymptotes of the function. Sketch a graph (+4) on the axes, labeling all key information.
13. f ( x)  2  32 2 x
13. Key Points: ______________ (+1)
______________ (+1)
______________ (+1)
Asymptote: __________________ (+1)
D: _________________________
(+1)
R: _________________________
(+1)
1
14. f ( x)  3  log 2  x  2 
4
D:_______________________(1)
R:_______________________(1)
A:_______________________(1)
14. Key Points: ______________ (+1)
______________ (+1)
______________ (+1)
Asymptote: __________________ (+1)
D: _________________________
(+1)
R: _________________________
(+1)