Poudre School District’s College Algebra Course Review
1. Perform the indicated operations
and simplify the result. Leave the
answer in factored form.
9x 9
2
6. Algebraically determine the equation
of the line in the form y mx b .
3x 3
22
7. Determine the equation of the line
perpendicular to the line you found
in #6 that passes through the point
( 3, 7) .
a. 33
1
33
11 9x 9
c.
3x 3
33
d.
x 1
b.
e.
2. Solve:
a.
b.
c.
d.
e.
8. Determine the equation of the circle
with endpoints of a diameter at the
given points (8, 2) and ( 4,4) .
9. Find the equation of the line that
connects the centers of the two
given circles.
circle #1: x 2 y 2 6x 12y 1 0
none of the above
2x 3 7x 2 15x 0 .
x 1.5, 5
x 0, 1.5, 5
x 5,0,1.5
x 1.5,0,5
circle #2: x 2
none of the above
3. Find the quotient and the remainder
of 8x 3 22x 2 7x 13 divided by
2x 3 .
4. Solve:
y
2
1
5y
3
4
y
For #6-8, consider the two points
(8, 2) and ( 4,4) .
2
1
y
2
5. Which expression below is
written in a
bi form?
1
a.
2i
5
1
b.
2i
5
c. 3 2i
d. 3 2i
e. none of the above
y 2 14x 8y
3 0
For #10-18, use the given graph of the
function f to answer the following
questions.
1
3y 4
4 7i
2 i
10.
11.
12.
13.
14.
Find the domain of f (x) .
Find the range of f (x) .
List the x-intercept(s).
Identify the y-intercept.
Find f ( 1) .
15. Is f
5
positive or negative?
2
16. State the interval for which f (x) is
negative.
2?
17. For what value(s) of x is f (x)
18. f (x) is increasing on what interval?
Poudre School District’s College Algebra Course Review
For #19-21, let f ( x ) x 2
19. Evaluate f (3) .
20. Find
f (x h)
h
5x 3 .
f (x)
and C
and simplify.
21. Solve f ( x )
3.
22. Algebraically determine whether the
following function is even, odd, or
neither.
h( x )
x3
2 x2 5
23. Given f (x) 2x 2 3x determine the
average rate of change from 1 to x.
Give answer in simplified factored
form.
24. Graph the following piecewise
defined function.
g ( x)
x 2 1 if x 1
3
if 0 x 1
x
if x
26. List the sequence of transformations
applied to the parent function.
27. Sketch a graph of f (x) with at least
3 points plotted.
28. State the domain and range of f (x) .
29. Solve the system.
y z
1
4 x 3y 2z 16
2x 2y 3z 5
30. Solve for x,
3 x
5 9
4 3
6
, B
8
2
0
8
7 1
1
2
3
1
2
y
,
4
. Find AB+C.
32. Find the inverse of the following
matrix:
3
2
5
7
.
For #33-35 assume an 8-cylinder Crown
Victoria gives 18 miles per gallon in city
driving and 21 miles per gallon in
highway driving and a family’s 300 mile
trip required 15.5 gallons of gasoline.
33. Identify the variables in the situation.
34. Write a system of equations based
on the situation.
35. Solve the system to find how many
whole miles were driven in the city?
0
2 x 5 3.
For #25-28, let f ( x )
25. State the parent function to which
transformations are applied.
x
31. Let A
8
36. Use the Corner Point principle to
maximize z 2x 5y subject to the
following constraints.
x 0
y 0
x 2y 6
9x 3y 27
a. z 13.8
b. z 12
c. z 14.6
d. z 15
e. None of the above
Poudre School District’s College Algebra Course Review
37. Perform each row operation in order,
(1) followed by (2) followed by (3),
on the given augmented matrix.
1
2
4
3
4
5
10
13 18
13 19
For #39-41, solutions must show
appropriate algebraic methods.
Let f (x) 2x 2 5x 2 .
39. Find the x-intercept(s).
5
40. Find the y-intercept.
41. Find the vertex of f(x).
(1)R2
3R1 R2
(2)R3
(3)R3
4R1 R3
2R2 R3
42. Is the vertex of f(x) a maximum or
minimum? Explain how you know
using complete sentences.
43. Which of the equations below
describes the graph shown?
1 2
a.
b.
c.
d.
4 5
0 1 1 3
0 0 1 5
1 2 4 5
0 1 1 3
0 0 1 5
1 2 4 5
0 1 1 3
0 0 1 5
1 2 4 5
0 1
0 0
1 3
1 5
e. None of the above
38. Find the quadratic function in the
form y a(x h) 2 k that has a
maximum point at (-1, -17) and
passes through (7, 1)
a.
y
b.
y
2(x 1) 2 17
1
(x 1)2 17
4
(x 7)2 1
(x 1)2 17
c. y
d. y
e. None of the above
a.
f (x)
b.
f (x)
c.
f (x)
d.
f (x)
e.
1
4
1
4
1
4
1
4
x 2
2
x 3
x 2
2
x 3
x 2 x 3
2
x 2 x 3
2
None of the above
44. Sketch the given function using the
intercepts and end behavior.
f ( x)
3x( x 2)2 x 4
For #45-48 let f ( x )
3
2 x 2 14 x 24
.
x 2 2 x 24
45. State the domain of f(x)
46. Find the x-intercept(s) and
y-intercept of f(x).
Poudre School District’s College Algebra Course Review
47. Find all asymptotes and/or holes.
48. Graph f(x). Be sure to plot at least
three points and show all
asymptotes.
49. One solution of x 3 5x 2 5x 1 0
is 1.
Find the two other solutions.
a.
2
3, 2
3
b.
4
3,4
3
c.
2 2 3,2 2 3
d.
4 2 3,4 2 3
e.
51. Find all the zeros of the function.
52. Write the polynomial as a product of
linear factors.
53. Use the given zero to find the all
remaining complex zeros of the
given function.
29 x 3 111 x 2 179 x 78
Given: 3 + 2i is a zero.
54. Find the indicated composite
f  g x for the pair of functions
f ( x)
x 9 and g ( x)
8x 13 .
a. 2 2 x 1
b. 8 x
9 13
c. 8 x
4
d. 2 2 x 1
e. None of the above
55. Find the inverse function of
f ( x)
b.
f 1 ( x)
c.
f 1 ( x)
d.
f 1 ( x)
5x
3
x
3x
3x
x
5x
3
2
x
5
2
2
5
2
x
56. Given the graph of
f ( x ) 3 x 2 4 , identify the
graph below that shows the graph of
f 1 . (Note the x and y scale is 2)
None of the above
3x 4
f 1 ( x)
e. None of the above
For #50-52 let y 3x 4 4 x 3 4x 2 4 x 1.
50. Determine the left and right hand
behavior of the graph of y .
h( x )
a.
3x 2
. (choices above)
x 5
Poudre School District’s College Algebra Course Review
57. Use the properties of logarithms to
find the exact value of the
expression
log 5 100 (log 5 8 log 5 2) .
a.
b.
c.
d.
e.
-2
2
4
-4
None of the above
58. Write 3 log 4 (2) 1 log 4 ( x 4) 1 log 4 ( x)
3
2
as a single logarithm with a
coefficient of 1.
62. Determine how long it takes a $3000
investment to double if it is invested
at 8% compounded semiannually.
a.
b.
c.
d.
e.
9.2 years
9 years
8.8 years
8.6 years
None of the above
63. Solve the equation e 2x 3 11 for x .
Round your answers to three
decimal places.
64. Solve the equation
log( x 3) log x 1 for x . Check
59. If 3
4x
2 what does 812 x equal?
60. An initial deposit of $3,000 is made
in a savings account for which the
interest is compounded
continuously. The balance will
double in seven years. What is the
annual rate of interest for this
account?
a.
b.
c.
d.
e.
4.3%
6.2%
8.1%
9.9%
None of the above
61. The half-life of silicon-32 is 710
years. If a sample presently
contains 50 grams, which
expression determines how much
silicon-32 material will remain after
1650 years?
ln(0.5)
710
ln(0.5)
b. 50e1650k where k
1650
ln(
0.5)
c. 1650e k where k
710
ln(0.5)
d. 710e1650k where k
50
a. 50e1650k where k
e. None of the above
for extraneous solutions.
65. Write the partial fraction
decomposition of the rational
expression.
5 x 4 5 x 3 18 x 2 11x 11
( x 1)( x 2 2) 2