Name:
Period:
C
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 2 2 x  4 , what does 82 x equal?
A. 1
2.
C.
B. -4
16
1. _____
1
64
D.
1
8
Where would the point (9, 2) for the parent function end up after being transformed according
2. _____
to f ( x)  2 log 3 x  1  1 .
A. (8, -3)
3.
E. None of these.
B. (8, -3)
Determine
C. (10, 3)
g  f  2 when
D. (10, -3)
E. None of these.
f ( x)   3x  15 and g ( x)  2 x 2  x
3. _____
A. 15
4.
A.
C.  3 5
B. 21
D. -15
 x4
Determine the Domain of the logarithmic function. H ( x)  log 2 

 x5
 5,4
B.  ,5 and [4,)
C. [ 4, )
D.  ,5 and 4,
E. None of these.
4. _____
E. None of these.
4 3
The volume of a hot air balloon as a function of radius, r, is given by V (r )  r . Find the volume of the
3
3 3
balloon as a function of time if the radius varies with time according to r (t )  t .
5. _____
2
5.
A.
V (t ) 
27 9
t
8
B. V (t ) 
27 6
t
6
C. V (t ) 
4 9
t
3
9
D. V (t )  2t
E. None of these.
6. Given f ( x) 
3x  2
2x  3
and g ( x) 
, determine  f  g x and its Domain.
x
3x  1
6. _______________________ (+3)
D: _______________________ (+2)
3x  2
and the Domain and Range of f
2x  1
your answer for the inverse is correct.
7. Determine the inverse of f ( x) 
1
( x) . Verify algebraically that
7. ________________________ (+3)
D: _______________________ (+1)
R: _______________________ (+1)
8. Determine the equation of the transformation for the parent function
.
8. ___________________________ (+5)
Solve the following equations algebraically.
2 x 1
9. 8  4 
32
x
x
 1 
11. log 
  7x  3
 1000 
1
x
   16
4
7
10. 2 
2 2 x 1

9. _______________ (+5)
10. _______________ (+5)

12. log 3 x 2  10 x  105  4
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)  2  32 x 3
13.
Points: ______________ (+1)
______________ (+1)
______________ (+1)
Asymptote: __________________ (+1)
14. f ( x)  3 
D: _________________________
(+1)
R: _________________________
(+1)
1
log 2  x  1
2
D:_______________________(1)
R:_______________________(1)
A:_______________________(1)
14.
Points: ______________ (+1)
______________ (+1)
______________ (+1)
Asymptote: __________________ (+1)
D: _________________________
(+1)
R: _________________________
(+1)