This document contains instructions and questions for a college algebra written assignment. It asks the student to answer multiple choice and free response questions related to topics covered in the textbook, including graphing functions, solving equations and inequalities, working with lines and systems of equations. The student is to show all work and refer to graphs in the textbook to answer some questions. The assignment is divided into sections covering various algebra concepts.

1. WA 6, p. 3
Name:
College ID:
Thomas Edison State College
College Algebra (MAT-121-GS)
Section no.:
Semester and year:
Written Assignment 6
Answer all assigned exercises, and show all work. An asterisk
indicates an exercise for which a graph pool is provided in the
assignment submission link.
Refer to graphs A–I on page 238 of the textbook to answer the
following questions. [18.75 points]
Which one is the graph of
yx
=? On what interval is it increasing?
Which one is the graph of
§
¨
yx
=
? What is the value of y when x = 1.5?
Which graphs of functions decrease over part of the domain and
increase over the rest of the domain? On what intervals do they
increase? decrease?

2. For the following piecewise-defined function, find (a)
(5)
f
-
, (b)
(1)
f
-
, (c)
(0)
f
, and (d)
(3)
f
.(See section 2.6, Example 2.) [12.5 points]
2 if 3
()
5 if 3
xx
fx
xx
-<
ì
=
í
-³
î

3. 2if 3
()31if 32
4if 2
xx
fxxx
xx
-<-
ì
ï
=--££
í
ï
->
î
Without graphing, determine whether each equation has a graph
that is symmetric with respect to the x-axis, the y-axis, the
origin, or none of these. [12.5 points]
4
23
yx
=-
15
yx
=+

4. Graph the function.*(See section 2.7, Examples6–8.) [12.5
points]
2
3
yx
=+
32
yx
=++
Let
2
()3
fxx
=+ and
()26
gxx
=-+. Find each of the following.(See section 2.8, Example1.)
[18.75 points]
()(5)
fg
+-
()(3)
fg
-

5. (5)
f
g
æö
ç÷
èø
For the following function, find (a)
()
fxh
+ (b)
()()
fxhfx
+-
, and (c)
()()
fxhfx
h
+-. (See section 2.8, Example4.) [12.5 points]
()411
fxx
=+
2
1
()
fx
x
=

6. Given functions f and g, find (a)
()()
fgx
o and its domain, and (b)
()()
gfx
o, and its domain.(See section 2.8, Example 4.)[12.5 points]
()2
fxx
=+,
42
()4
gxxx
=+-
2
()4,()
fxxgx
x
=+=-
WA 5, p. 4
Name:
College ID:
Thomas Edison State College
College Algebra (MAT-121-GS)

7. Section no.:
Semester and year:
Written Assignment 5
Answer all assigned exercises, and show all work. An asterisk
indicates an exercise for which a graph pool is provided in the
assignment submission link.
For the points P and Q, find (a) the distance d(P,Q) and (b) the
coordinates of the midpoint of the segment PQ. (See section 2.1,
Examples2 and 5(a).) [8 points]
P(–4, 3), Q(2, –5)
(7,83),(57,3)
PQ
--
Determine whether the three points are collinear.(See section
2.1, Example 4.)[4 points]
(–1, 4), (–2, –1), (1, 14)
For the following equation, (a) give a table with at least three
ordered pairs that are solutions, and (b) graph the equation.*
(See section 2.1, Examples7 and 8.)[8 points]

8. 2
2
yx
=+
4
yx
=-+
(a) Find the center-radius form of the equation of the circle, and
(b) graph it.* (See section 2.2, Examples1 and 2.)[8 points]
center (0, 0), radius 9
center (–3, –2), radius 6
Decide whether or not the equation has a circle as its graph. If it
does, give the center and the radius. If it does not, describe the
graph.(See section 2.2, Examples3–5.)[8 points]
22
121025
xyxy
+-+=-
22
4480
xyxy

9. ++++=
Decide whether the relation defines a function, and give the
domain and range. (See section 2.3, Examples 1–4.) [4 points]
Let
()34
fxx
=-+and
2
()41
gxxx
=-++. Find and simplify each of the following.(See section 2.3,
Example 6.)[8 points]
(3)
f
-

10. (32)
ft
-
Use the graph of
()
yfx
=to find each function value: (a)
(2)
f
-, (b)
(0)
f, (c)
(1)
f, and (d)
(4).
f(See section 2.3, Example 7(d).) [4 points]
Determine the intervals of the domain for which the function is

11. (a) increasing, (b) decreasing, and (c) constant.(See section 2.3,
Example 9.)[4 points]
Graph the linear function.* Identify any constant functions.
Give the domain and range. (See section 2.4, Examples 1 and
2.) [4 points]
()3
fx
=
Find the slope of the line satisfying the given conditions. (See
section 2.4, Example5.)[4 points]

12. through
(5,3)
-
and
(1,7)
-
Graph the line passing through the given point and having the
indicated slope.* Plot two points on the line. (See section 2.4,
Example 7.) [8 points]
through
3
(2,3),
4
m
--=-
through
9
,2
4
æö
ç÷
èø, undefined slope
Write an equation for the line described. Give answers in
standard form. (See section 2.5, Examples 1 and 2.) [12 points]
through (2, 4),

13. 1
m
=-
through
3
(4,3),
4
m
-=
through
(5,1),
undefined slope
Give the slope and the y-intercept of the line. (See section 2.5,
Example 3.) [4 points]
2316
xy
+=
Write an equation (a) in standard form and (b) in slope-intercept
form for the line described.(See section 2.5, Example 6.) [8
points]
a. through
(3,2),
-

14. parallel to
25
xy
-=
b. through
(4,4),
-
perpendicular to
4
x
=
Determine whether the three points are collinear by using
slopes. [4 points]
(0,7), (3,5), (2,15)
---
WA 4, p. 3
Name:
College ID:
Thomas Edison State College
College Algebra (MAT-121-GS)
Section no.:
Semester and year:

15. Written Assignment 4
Answer all assigned exercises, and show all work.
Dimensions of a garden (see section 1.5, Example 1)—An
ecology center wants to set up an experimental garden using 300
m of fencing to enclose a rectangular area of 5000 m2. Find the
dimensions of the garden. [4 points]
Width of flower border (see section 1.5, Example 1)—A
landscape architect has included a rectangular flower bed
measuring 9 ft by 5 ft in her plans for a new building. She wants
to use two colors of flowers in the bed, one in the center and the
other for a border of the same width on all four sides. If she has
enough plants to cover 24 ft2 for the border, how wide can the
border be? [4 points]
Height of a kite (see section 1.5, Example 2)—Grady is flying a
kite on 50 ft of string. Its vertical distance from his hand is 10
ft more than the horizontal distance from his hand. Assuming
that the string is being held 5 ft above ground level, find the
distance from Grady and its vertical distance from the ground.
[4 points]

16. Height of a projectile (see section 1.5, Examples 3 and 4)—A
projectile is launched from ground level with an initial velocity
of v0 feet per second. Neglecting air resistance, its height in
feet t seconds after launch is given by
2
0
16.
stvt
=-+
Find the time(s) that the projectile will (a) reach a height of 80
ft and (b) return to the ground for the given value of v0. Round
answers to the nearest hundredth if necessary. [4 points]
0
16
v
=
Solve each equation. (See section 1.6, Examples4–6.) [16
points]
41321
xx
+=-

17. 240
xx
-+=
23122
xx
=+-
2522
xx
-=+-
Solve the equation. (See section 1.6, Examples 8 and9.) [4
points]
42
310250
xx
+-=
Solve the equation for the indicated variable. Assume all
denominators are nonzero. [4 points]
2/32/32/3
,

18. xya
+=for y
Match the following inequality with its equivalent interval
notations (a–d). [4 points]
(,6]
-¥-
(,6)
-¥-
[6,)
-¥
(,6]
-¥
The three-part inequality a < x < b means “a is less than x and x
is less than b.” Which one of the following inequalities is not
satisfied by some real number x? [4 points]
310
x
-<<
06
x
<<
31
x
-<<-
810
x

19. -<<-
Solve each inequality. Write each solution set in interval
notation. (See section 1.7, Examples 1 and 2.) [8 points]
432
xx
-+³-+
25
1
8
x
x
-
£-
-
Break-even interval—Find all intervals where the product will
at least break even. (See section 1.7, Example 3.) [4 points]
The cost to produce x units of baseball caps is
1006000,
Cx
=+
while the revenue is
500.
Rx

20. =
Which of the following inequalities has solution set
?
Æ[4 points]
2
(3)0
x
-³
2
(56)0
x
-£
2
(64)0
x
+>
2
(87)0
x
+<
Solve the following rational inequality. Write the solution set in
interval notation. (See section 1.7, Examples 8 and 9.) [4
points]

21. 6
2
35
x
-
£
-
Solve each equation. (See section 1.8, Example 1.) [8 points]
733
x
-=
23
1
34
x
x
+
=
-
The equation
563
xx
-=cannot have a negative solution. Why? [4 points]

22. Determine the solution set of each equation by inspection. [8
points]
xx
-=
xx
-=
2
xx
=
9
x
-=
Solve the inequality. Give the solution set using interval
notation. (See section 1.8, Example 2.) [8 points]
3
1
5
x
+<

23. 734
x
->
Write the statement as an absolute value equation or inequality.
(See section 1.8, Example 5.) [4 points]
z is no less than 5 units from 4.