College AlgebraDepartmental Review Sheet
Fall 2005
(College Algebra, 9
th
Edition
.
Lial, Hornsby, and Schneider.
Pearson, Addison Wesley, 2005.)
Unless otherwise stated, all work should be done algebraically, all work should be shown, and exact answers should be
given.
No formula sheets or note cards are allowed for use during the final exam.
Each problem on this review sheet is
matched with its corresponding objective in the course outline and the section of the textbook in which it appears.
[Obj 1, Sec 2.4]
1.
Write an equation for the line described.
Give your answer in slopeintercept form.
a.
through (1, 3)
with slope – 2
b.
through (  8, 4) with undefined slope
c.
through
(
29
3
,
2
and
(
29
1
,
5

d.
horizontal through (2, 5)
e.
through (2,6) perpendicular to 3x+2y=4
f.
through (2,6) parallel to 3x+2y=4
[Obj 2, Sec 2.6]
2.
Write an equation of a function with the same basic shape as
x
y
=
but moved left 3 units, down 1 unit, and
vertically stretched by a factor of 4.
3.
Explain how the graph of
2
)
3
(
2



=
x
y
can be obtained from the graph of
2
x
y
=
.
List all appropriate
translations (be specific about direction and number of units), reflections, shrinks and/or stretches.
[Obj 3, Sec 3.3]
4.
Given
8
2
5
)
(
2
3

+
+
=
x
x
x
x
f
a.
List the possible rational zeros.
b.
Find the zeros of f(x).
Show all work and give exact values.
c.
Factor
)
(
x
f
into linear factors.
5.
Given
8
2
61
15
)
(
2
3

+
+
=
x
x
x
x
f
a.
List the possible rational zeros.
b.
Find the zeros of f(x).
Show all work and give exact values.
c.
Factor
)
(
x
f
into linear factors.
[Obj 4, Sec 1.4]
6.
Solve algebraically, show all your work, and give an exact answer:
4x
2
= 12x  11
[Obj 4, Sec 1.6]
7.
Solve algebraically, show all your work, and give an exact answer:
x
x
x
x
x
+
=
+
+
+
2
1
2
1
3
4
[Obj 4, Sec 4.2]
8.
Solve algebraically, show all your work, and give an exact answer:
3
2
2
9
27

=
x
x
[Obj 4, Sec 4.3]
9.
Solve algebraically, show all your work, and give an exact answer:
2
16
1
log