MATH 0310
Intermediate Algebra
Homework Assignments
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LSC–North Harris
Last Revision: 12/10/13
MATH 0310 Homework Assignments
Table of Contents
Chapter 2
Absolute Value Equations
2.5
Absolute Value Equations
Chapter 3
3.3
3.4
3.5
3.6
3.7
3.8
Factoring Polynomials and Factorable Quadratic Equations
GCF and Grouping
Factoring Binomials
Factoring Trinomials
Factoring Summary
Quadratic Equations
Applications – Quadratic Equations
Chapter 4
4.1
4.2
4.3
4.4
4.5
4.6 and 4.7
4.8
4.9
Rational Expressions and Rational Equations
Integer Exponents
Reducing Rational Expressions
Multiplying and Dividing Rational Expressions
Adding and Subtracting Rational Expressions
Complex Fractions
Division of Polynomials
Rational Equations
Applications-Rational Equations
Chapter 5
5.1
5.2
5.3
5.4
5.5
5.6
5.7
Exponential and Radical Expressions and Radical Equations
Rational Exponents
Radicals
Simplify Radical Expressions
Adding and Subtracting Radical Expressions
Operations with Radical Expressions
Radical Equations
Complex Numbers
Chapter 6
6.1
6.2
6.3
6.4
6.5
2.2
6.7
Linear Relations and Functions
Cartesian Coordinate System
Relations and Functions
Function Notation and Combinations of Functions
Linear Functions
Equations of Lines
Linear Inequalities in One Variable
Linear Inequalities in Two Variables
Chapter 7
7.3
7.4
Solving Quadratic Equations
Extraction of Roots Method and Completing the Square Method
Quadratic Formula
MATH 0310 Homework Assignments
MATH 0310 Homework Assignments
Ch 2
2.5
Absolute Value Equations
Absolute Value Equations
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the solutions of the following equations.
3. z  23
42. 2 5 x  1  14
6. t  4
45. 2 x  4  2  11
9.  s  0
48. 2  3x  4  1
12. 3z  6
51. 2 x  3  5  7
15. 5s  13
54. 4  x  2  2
18. 2 x  34
57. 10  5 6  4 x  12
21. 4 s  24
60. 1.8 23.9 x  13.1  6.005  394
24. 5 z  40
63. 6  x  4 x  3
27. x  5  9
66. 3x  1  5  2 x
30. x  6  6
69.
33. x  7  9
72. x  2  x  1
36. 2 x  6  0
75.
39. 2 3  4 x  15
1
x5  x2
2
1
1 1
1
x  x
2
3 2
4
MATH 0310 Homework Assignments
Ch 3
3.3
Factoring Polynomials and Factorable
Quadratic Equations
GCF and Grouping
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Factor completely.
1. 10 x2  35
17.
2. 8x3  18xy  2 x
18.
3. 6 x5  18x3  10 x2
19.
4. 4 x( x  2 y)  6 y( x  2 y)
20.
5. 2 x( x  3)  ( x  3)
21.
6. 8 y 2 z (1  5x)  6 yz 3 (1  5x)
7. 15x( y  3)  5z(3  y)
8. 2ax  3bx  2ay  3by
9. 6cf  2cg  6df  2dg
10. 4 x  15xy  3x 2  20 y
11. 3x2 y  5x2 y 2  12 xy 2  20 xy3
12. 3 y3  7 y 2  18 y  42
13. 8x6  12 x4  40 x3  60 x
14. 54 y3  6 x4  27 x3 y  12 xy 2
15.
16.
(
)
(
)
(
)
(
)
MATH 0310 Homework Assignments
3.4
Factoring Binomials
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Factor completely.
1. x 2  9
11. 54 x3  128 y3
2. 36 x 2  49 y 2
12. 375x3  3
3. 27 x3 y  12 xy 3
13. x2 (2 x  3)  (2 x  3)
4. 3x 2  48
14. x3 ( x  6)  8( x  6)
5. 81x 4  16 y 4
15. 5x3  2 x2  45x  18
6. ( x  3)2  49
16. 3x3  4 y3  4 x2 y  3xy 2
7. (2 x  3 y)2  9 z 2
17. 3x4  5x3  3x  5
8. x3  64
18. 4 x4  3x3  32 x  24
9. 8 x3  1
19. 4 x5  x3  32 x2  8
10. 64 x3  27 y3
20. 7 x5  7 x3  28x3 y 2  28xy 2
MATH 0310 Homework Assignments
3.5
Factoring Trinomials
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Factor completely.
1. x2  9 x  14
11. 9 x2  30 x  25
2. x 2  9 x  8
12. 2  17 x  9 x2
3. x2  x  7
13. 6 x2  13x  15
4. x2  6 x  9
14. 20 x2  60 x  35
5. 3x2  24 x  21
15. 15x3  42 x2  9 x
6. 2 x3  16 x2  32 x
16. 9 x 2  16 xy  4 y 2
7. x 2  6 xy  5 y 2
17. x4  2 x2  3
8. 6 x2  13x  5
18. 4 x4  7 x2  2
9. 12 x2  25x  7
19. 6 x2  19 x  15
10. 9 x2  15x  4
20. 10 x2  19 x  6
MATH 0310 Homework Assignments
3.6
Factoring Summary
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Factor Completely.
1. 2 x2  7 x  3
11. x 2  6 xy  9 y 2
2. x 2  7 xy  8 y 2
12. 4 x2  4 x  3
3. 3  2 x  1  11 2 x  1  20
13. 25x 2  16 y 2
4. 125x3  8 y3
14. x2  10 x  25  81y 2
5. x 2  xy  12 y 2
15. 3x2  8xy  4 y 2
6. x 2  3xy  10 y 2
16.
7. 18x3 y3  6 x2 y 4  4 xy5
17. 4 x2  24 x  36
8. x2  10 x  25
18. 6m5n4  15m3n6  3m2 n4
9. 64 x3  1
19.
2
10. 2 x 2  xy  3 y 2
 x  1
2
 x  4
3
 4 y2
 125 y 3
MATH 0310 Homework Assignments
3.7
Solving Quadratic Equations by Factoring
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Solve by factoring.
1. x2  6 x  8  0
8. x2  5x  4  10
2. 2 x2  12 x  32  0
9. 8x2  13x  9  5x  4
3. 6 x2  2 x  0
10. 3x2  5x  20  2 x2  3x  4
4. 4 x2  9  0
11. 9 x2  7 x  7  3x( x  4)
5. 2 x2  7 x  4  0
12. 3x2  8x  31  (2 x  3)( x  7)
6. 6 x2  41x  7  0
13. (2 x  5)( x  4)  ( x  7)( x  4)
7. 12 x2  31x  9  0
MATH 0310 Homework Assignments
3.8
Applications
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the solutions.
1.
2.
3.
4.
5.
6.
⁄
7.
8.
(
)
MATH 0310 Homework Assignments
Ch 4
4.1
Rational Expressions and Rational
Equations
Integer Exponents
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Evaluate each of the following. Your answers should have NO exponents.
1. 22  23
7. (2)3
14. 22  41
(7) 4
2.
(7)5
8. (3)4
15. 80  81  8
1 2
3. (4 )
4. 82
9. 3
16. 5  5  5
10. (3)3
2
17.  
3
11. 33
5. (8)2
3
12. 2  4
6. 2
1
0
4
5
18.  
8
1
3
4
19.  
3
2
5 2
20. 1
3
3
1
13. 42  31
Simplify each of the following. Your answers should have no NEGATIVE
exponents.
 8 x9 y 3 
21.  3 2 
 4x y 
2
 2x4 
24.  2 
 5y 
22 x 3 y 4
27. 1 1 2
8 x y
3
22.
(3x2 y 2 )1 (4 xy3 )2
 5 x 3 y 
25.  2 2 
 3x y 
23. (8 x0 y 4 )0
8 x3 y 2
26.
10 x 6 y 5
28.
 2x y 
5x y 
29.
 3x y 
 2x y 
3
3
4 4
0
7 2
4
4
7 3
3 4
 40 x 2 y 6 
30. 
3 4 
 8x y 
2
MATH 0310 Homework Assignments
4.2
Reducing Rational Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Reduce the following expressions to lowest terms.
8x4 y 2
1.
6 xy 3
6x2  7 x  5
8.
2 x2  x
9ab 2 c3
2.
4ab3c
9.
3x3  x 2 y
3. 2 2
x y  2 xy 3
4 x 2  12 x  9
10.
2 x 2  11x  12
3x  6 y
4.
3x
11.
4 x3 y  4 x 2 y
5.
2 xy 2  2 x 2 y 2
2 x 2  5 x  12
12.
9  4 x2
x2  5x  6
6. 2
x  4 x  21
13.
6x2  7 x  3
7.
4x2  9
27 x3  1
14.
6x2  4x  2
x 2  3x  10
4  x2
3x 2  9 x  30
6 x 2  30 x
x3  8
3x 2  2 x  8
MATH 0310 Homework Assignments
4.3
Multiplying and Dividing Rational Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated operations and reduce to lowest terms.
1.
5 xy 2 3x 4 y 7 14 x5 y 2


7a3b 4 6a 2b6 15a 4b
2.
5 x3 y 5 14ab7 a 2b 2


8a3b 2 9 xy8 12 xy
3.
2x  2 x  3

5 x  15 xy  y
10 x 2 y 2  5 xy 2
6x  3

4.
8  4x
12 x  24
5.
10 x 2  17 x  3 5 x 2  41x  8

2 x2  7 x  6
2 x2  x  6
6.
x2 1
3x 2  2 x  8

3x 2  x  4 5 x  5 x 2
7.
6  23x  4 x 2 3x 2  x  24

3x 2  10 x  48 8 x 2  6 x  1
8.
3x 2  10 x  8
 (2 x  5)
2 x 2  3x  20
9.
x3  8
3x 2  2 x  1

x 2  2 x  3 3x 2  5 x  2
10.
x3  1
2 x 2  3x  20 2 x 2  3x  5


2 x 2  11x  12 8 x3  12 x 2
4 x2  9
MATH 0310 Homework Assignments
4.4
Adding and Subtracting Rational Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated operations and reduce to lowest terms.
1.
3
7

2x 2x
11.
5
2

x2 x3
2.
2n 9n

xy xy
12.
3
5

2x  5 x  3
3.
x
3x  5

4x  7 4x  7
13.
x  2 x 3

2x  3 x  6
4.
5x  1
2x  9
 2
2
2 x  x  11 2 x  x  11
14.
x  1 3x  2

2x  5 2x  3
5.
x2  2 x
1

x 1
x 1
15.
2
5
 2
x  4 x  5 x  2 x  15
6.
7x
3x

y2 2 y
16.
4x
1
 2
3x  5 x  2 3x  13x  4
2 x 2  8 x 2  x  12

7.
x 5
5 x
17.
2x  3
x2
 2
2
x 1 x  6x  5
2 x2  5 x2  2

8.
x 1
1 x
18.
3x  5
x 1
 2
x  x  12 x  5 x  6
19.
x 1
x2
 2
6x  7 x  2 2x  7 x  3
20.
x 1
4x  5
 2
4 x  4 x  15 8 x  10 x  3
8
3

9.
5x 2 y
10.
3
7
 2
2
4 xy 3x y
2
2
2
2
2
MATH 0310 Homework Assignments
4.5
Complex Fractions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Simplify the following fractions.
5
1. 7
45
16
5
3
 2
2x 2x
8.
15
9
2  2
2x 2x
1
3x
2 y2
2.
5x4
4 y3
9.
2 x  3x
y2  y
3.
8 x 4  12 x 3
3 y3  3 y 2
2
8 xy  4 y
6 xy 2
4.
12 x 2 y  6 xy
9 x2 y 2
3
x
5.
7
1
x
2
2 2

x y
6.
4
2 2
x y
1 1

x y
7.
1
1
 2
2
x
y
2x  y
2 1

y x
1
9x2
10.
1  3x
1
3 1

2
x
3
11.
x3
1 1

x y
12.
x y
5
4
2
2

h
13.
h
4
3
14. 2 x  1
5
2
2x 1
MATH 0310 Homework Assignments
4.6 and 4.7
Division of Polynomials
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated divisions using LONG division method.
1.
24 x 2  62 x  36
4x  7
40 x 2  44 x  17
2.
5x  3
3.
2 x3  13x 2  10 x  19
2x  3
19  8 x  21x 2  12 x3
4.
4x  7
5.
4 x2  7
2x  3
4 x3  x  7
6.
2x  3
7.
6 x3  20 x 2  19
2x  6
2 x 4  x3  3x 2  9 x  13
8.
x2  x  3
Perform the indicated divisions using SYNTHETIC division.
x 2  3x  5
9.
x2
10.
2 x3  7 x 2  x  6
x 3
x3  7 x  4
11.
x2
12.
3x3  11x 2  5 x
x4
(Hint: need a place holder for the constant)
x 4  2 x3  5 x 2  x  5
13.
x2
14.
2 x 4  3x3  x 2  7 x  5
x 1
6 x 4  7 x3  11x 2  2 x  3
15.
1
x
6
MATH 0310 Homework Assignments
4.8
Rational Equations
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Solve the following equations. Do not forget to check solutions.
1.
3 9

2x 8
10.
5 1
 2
x 2 3x
2.
3
1 11


2 x 3x 12
11.
2
x
36

 2
2x 1 x  4 2x  7 x  4
3.
x 1 x  5

2
4
12.
4x
x
12

 2
x 1 x  3 x  2x  3
4.
2
3
5


2x 1 x  4 2x 1
13.
3x  6 1

2x  5 x
5.
2
1
3


x  1 3x  2 3x  2
14.
x  3 x 1

9x 1
7
6.
5
1
6

 2
2x  1 2x 1 4x 1
15.
9x  3
x

10 x  30 x  3
7.
1
2
1

 2
x 4 x  1 8x  2 x
16.
2
4
4


x  3 x 1 3
8.
2x 1 2x 1
10

 2
x2
x2 x 4
17.
1
5
3


x 5 x 2 2
9.
1 1 1


x2 6x 6
18.
x2 x5 5


2x 1 x  3 3
MATH 0310 Homework Assignments
4.9
Applications-Rational Equations
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the solutions to the following problems.
1. The sum of a number and its reciprocal is
25
. What is the number?
12
2. The sum of the reciprocals of two consecutive integers is
integers?
7
. What are the
12
3. The sum of the reciprocals of two consecutive even integers is
integers?
7
. What are the
24
4. Tameka can mow her yard in 2 hours. Her brother Dante can mow the yard in 3
hours. Working together, how long will it take them to mow the yard?
5. Brittany can prepare her report in 1 1
2
hours. Her co-worker, Firza, can prepare
the report in 6 hours. Working together, how long will it take them to prepare
the report?
6. Working together Debbie and Jim can clean the house in 4 hours. Working
alone, Debbie can clean the house in 5 hours. How long does it take Jim to clean
the house?
7. Working together, Elmer and his son can paint their house in 3 days. Working
alone, Elmer can spray paint the house in 4 days. How long will it take his son,
using a brush, to paint the house by himself?
8. Colonel Scanlon can fly his plane 300 mi with the wind in the same time that he
can fly it 240 mi against the wind. If the speed of his plane is 180 mi/hr, what is
the wind speed?
9. Maureen can fly her plane 250 mi with the wind in the same time that she can fly
it 200 mi against the wind. If the speed of her plane is 90 mi/hr, what is the wind
speed?
MATH 0310 Homework Assignments
Ch 5
5.1
Exponential and Radical Expressions and
Radical Equations
Rational Exponents
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Evaluate each of the following, if possible.
1. 36
1
1
 25 
2.  
 49 
3.
 9 
4. 4
1
1
1
15. 25
1
3
16.
1
3
2
2
 49 
3
2
2
 1 
10.  
 32 
1
14. 49
3
2
2
6. 16
1
 27 
9.   
 8 
5. (16)
7. 64
 8 
8. 

 125 
2
1
11. 4
4
5
 16 
18.  
 81 
2
1
3
2
4
1
19. 25 3  25
3
1
13.   
 16 
3
17. 100
5
2
12. 8
4
1
3
2
20.
27
27
1
1
1
6
2
6
Simplify each of the following. Your answers should have no NEGATIVE
exponents.
3
21. x 4  x
22.
23.
 4x 
3
2x
2
3x
1
1
12
1
2
 
 8x
1
24.
6 x3 y
1
 25 x3 
27.  1 
3
 9y 
2
1
4x 3 y2
3
1
25. 2 x 3  5 x
1
6
1
 27 x 1 

26. 
3
2 
 8y

2
2
29. 5 x 4  7 x
3
4
1
3
2
3
MATH 0310 Homework Assignments
5.2
Radicals
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Evaluate each of the following, if possible.
1.
100
5.
2.
121
4
6.
27
7.
3.
4.
3
3
64
8.
49
3
3
8
27
9.
4
5
10.
5
32
243
14.
11.
4

1
81
15.
32
100
49
13.
43
132
12.
1
16
3
3
27
64
81
Convert the following expressions to radicals.
16. 7
17.
2
3
 5
1
5
18.
 4xy 
19.
 2x 
1
3
4
2
Convert the following radicals to expressions with rational exponents.
Simplify where possible.
20.
7
21.
 x
22.
4
3
k4
 7x y 
23.
24.
8
3
3
a15
6
MATH 0310 Homework Assignments
5.3
Simplify Radical Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Simplify the following radicals.
1.
48
2.
80
3.
3
16
4.
4
80
5.
3
128x
7
6.
x2 y 2
7.
32x 7 y 4
8.
9.
10.
11.
12.
13.
14.
5
8x
15.
16.
3
1
4
17.
3
1
2
18.
2
9x
19.
3
7x
20.
2x
3 y3
1
3
21.
8x4
5 y2
3
12
22.
3
7
8x
3
5
23.
3
16
3x 2
3
6
24.
3
3y2
5x4
144x5 y 7 z 8
3
81x9 y 2 z 4
5
x
25.
49 x3
9 y3
MATH 0310 Homework Assignments
5.4
Adding and Subtracting Radical Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated operations.
1. 3 7  5 7  8 7
2. 2 15x  7 15x  5 15x
3. x 3 10 y  8x 3 10 y
4. 5 12  2 27  3 3
5. 5 8  18  2 32
6.
7.
3
32  3 108
27 x  2 12 x  2 48x
8. x 18x  5 2 x3  2 x 8x
9.
27 x  2 12 x  150 y  4 24 y
10. x 20 x 2  x 45  2 500
11.
1
5 2
2
12.
3
 80
5
13.
1 3
 108
2
3
14.
3
5 2 27

3
3
15.
2
4
50

2
2
MATH 0310 Homework Assignments
5.5
Operations with Radical Expressions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated multiplications and simplify your answers.


7.
3


8.

9.
3 
10.

11.
5
12.
3  4
1.
3 2 5
2.
x 3 x
3.
 2  7 
4.

5.
2
3 4 5 3 2 6 7
6.
2
x 3 y 4 x 5 y
5 7

8 3

10  2





2 6 3
2 x 7


2
2
x2
5 3

2


2x  6
13.
1
32
17.
x 5
x 4
14.
2
3 5
18.
3 2
6 3
15.
x
x y
19.
2 3
2 3
20.

3 6 5 3 6
Rationalize the denominator of the following radicals.
16.
5 3
x y
x y
5 37
2 34

2

MATH 0310 Homework Assignments
5.6
Radical Equations
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the solutions(s) of the following radical equations.
1.
2x 1  3
10.
x 2  8x  26  5  x
2.
x2  7  4  0
11.
2x  5  x  3
3.
3x  7  2  0
12.
x  8  x  4
4.
3
3x  1  4
13.
3x  5  1  3 x
5.
3
3x 2  10 x  2  0
14.
3 x  x  3
6.
4
3x  5  3
15.
x4  x  6
7.
3x  40  x
16.
x
8.
2 x2  2 x  3  x
17.
 2x
9.
4 x2  x 1  1  2 x
18.
2
 4 x  5
2
3
2
 5x  6
3
 64
2
x2  x  2
8
MATH 0310 Homework Assignments
5.7
Complex Numbers
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Perform the indicated operations.
9.  5  2i    3  i 
1.  121
2.
10. 7(3  9i)
9  16
11. 2i  4  7i 
3.  50  12
4.
12.  6  i  3  4i 
21  21
5. 5 12  6
6.
7.
13.
 21
1
 5  3i  2  4i 
14.  2  5i  2  5i 
25 49
36
8. (2  3i)  (5  6i)
15.

16.
 2  3i 
17.

3 i
3 i


3 i

2
2
Rationalize the denominators.
18.
5
3i
22.
3
2  3i
26.
9  17i
2i
19.
5  3i
i
23.
2i
1  3i
27.
2  5i
1  4i
20.
4i
2i
24.
4i
3  5i
21.
1
4  2i
25.
3  4i
3i
MATH 0310 Homework Assignments
Ch 6
6.1
Linear Relations and Functions
Cartesian Coordinate System
1. Find the ordered pairs associated with the given points:
Make a table of values and graph the following equations on graph paper provided.
(next page)
2. y  2 x  3
7. y  9  x 2
3. x  2 y  4
8. x  1  y 2
4.
1
x2 y
2
5. 2 x  3 y  0
6. y  x 2  5
9. y  x  4
10. y  x  2
MATH 0310 Homework Assignments
6.1
(Continued)
2. y  2 x  3
3. x  2 y  4
4.
5. 2 x  3 y  0
6. y  x 2  5
7. y  9  x 2
8. x  1  y 2
9. y  x  4
10. y  x  2
1
x2 y
2
MATH 0310 Homework Assignments
6.2
Relations and Functions
Do all work on notebook paper. All work should be neat and organized.
Write the following sets as sets of ordered pairs and identify the domain
and range.
3

1. V  ( x, y ) : y  2 x  7, x  5,0, 2,1, 
2

2. Z  {( x, y) : y  x  3, x  2,0, 2}
1

3. X  ( x, y ) : y  2 x  1, x  1,3,5, 
2

Determine the domain and range of each relation whose graph is given.
Determine which of the following are graphs of functions.
4.
5.
MATH 0310 Homework Assignments
6.2
(Continued)
6.
7.
8.
9.
MATH 0310 Homework Assignments
6.2
(Continued)
10.
11.
12.
13.
MATH 0310 Homework Assignments
6.2
(Continued)
14.
15.
16.
17.
MATH 0310 Homework Assignments
6.2
18.
(Continued)
19.
MATH 0310 Homework Assignments
6.3
Function Notation and Combinations of Functions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
For the given functions, find the following values:
f (2), f (1), f (0), f (1), f (a ), f (a  h)
1. f ( x)  2 x  3
4. f ( x)  5  x 2
2. f ( x)  3  x
5. f ( x)  2 x 2
3. f ( x)  x 2  2
 f
( x) .
g
 
Find ( f  g )( x ), ( f  g )( x ), ( f  g )( x ), 
6. f ( x)  2 x 2  5x  1 , g ( x)  x  2
8. f ( x)  2 x  3 , g ( x)  x  11
7. f ( x)  x 2  5 , g ( x)  x2  9
9. f ( x)  x3  3x  5 , g ( x)  2 x  1
Let f ( x )  3 x  1, g( x )  3 x  5 x  1 , m( x )  x  4 , and p( x )  2 x  1.
Find the following:
2
2
10. f (2)
16. (m  p)(1)
22. f (a)
11. m(3)
17. ( g  f )(0)
23. f (a  h)
12. 5 f (2)  4m(3)
18. g ( x)  m( x)
13.
 f (2)
3
19.
14. g (3)
 m(3) 
15. 

 g (3) 
m( x )
p( x)
24.
f ( a  h)  f ( a )
h
25. g (a)
20. g (2 x)
26. g (a  h)
21. p(3x)
27.
2
g ( a  h)  g ( a )
h
MATH 0310 Homework Assignments
6.4
Linear Functions
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Solve for y. Identify the slope and y-intercept.
1. 2 x  y  6
4. 2 x  3 y  8
2. 3x  4 y  8
5. 4 y  12  0
3. x  3 y  0
6.
1
3
y x2  0
3
4
Find the x-intercept and y-intercept.
7. 3x  4 y  6
8. 4 x  5 y  10
9. 5x  3 y  0
10. y  2 x  5
11.
2
1
y  x  3
3
5
Find the slopes of the lines passing through the following points.
12. (6,0) and (0, 3)
15. (5, 2) and (9, 2)
13. (4,1) and (3, 5)
16. (3,1) and (3,10)
14. (3, 7) and (6, 2)
MATH 0310 Homework Assignments
6.4
(Continued)
Graph the following lines. Find the slope and y-intercept.
17. 3x  y  2
m=
18. x  2 y  4
b=
20. 3x  5 y  0
m=
m=
b=
19. 4 y  3x  8
b=
21. y  2 x 
b=
23. x  3
m=
24. 3 y  6  0
5
2
m=
b=
22. y  4
b=
m=
b=
m=
m=
b=
25. 5x  15  0
m=
b=
MATH 0310 Homework Assignments
6.5
Equations of Lines
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the equations of the following lines. Write answers in slope-intercept
form.
1. m  5 ; y-intercept 
1
2
2. m  1; y-intercept  9
4. m  0 ; y-intercept
 11
5. m  0 ; y-intercept 
2
5
1
3. m  ; y-intercept  3
2
Find the equations of the following lines. Write answers in slope-intercept
form when possible.
6. m  3 ; through ( 1, 2)
9
7. m  ; through (3, 8)
2
2
8. m   ; through (5, 3)
3
9. m  0 ; through ( 4, 12)
10. m is undefined ; through (3, 7)
Find the equations of the lines passing through the given points. Write
answers in slope-intercept form when possible.
11. (2, 4) and (5,7)
12. (8,6) and (4, 3)
13. (0,0) and (2,3)
14. (8, 4) and (3, 4)
15. (5,3) and (5, 6)
MATH 0310 Homework Assignments
6.5
(Continued)
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Find the equations of the lines passing through the given points parallel to
the given line. Write answers in slope-intercept form when possible.
16. Through (1, 2) ; parallel to y  3x  4
17. Through (3,11) ; parallel to 5 x  4 y  8
18. Through (2,5) ; parallel to 3x  7 y  21
19. Through (3, 7) ; parallel to y  12
20. Through (8, 9) ; parallel to x  5
Find the equations of the lines passing through the given points perpendicular to
the given line. Write answers in slope-intercept form when possible.
21. Through (1, 2) ; perpendicular to y  3x  4
22. Through (3,11) ; perpendicular to 3x  5 y  10
23. Through (2,5) ; perpendicular to 4 x  3 y  21
24. Through (3, 7) ; perpendicular to y  4
25. Through (8, 9) ; perpendicular to x  7
MATH 0310 Homework Assignments
2.2
Linear Inequalities
Find and graph the solutions of the following inequalities. Express your answers
using interval notation.
1. 4 x  2  10
2. 6  2x   x
3.
1
5 3
x 3  x
5
4 2
Find and graph the solutions of the following inequalities. Express your
answers using interval notation.
4. 7  x  4  1
5. 5  2  3x  11
Find and graph the solutions of the following compound inequalities. Express
your answers using interval notation.
6. 5x  2  4 and 2 x  7  3
7. x  1  4 or 1  x  4
MATH 0310 Homework Assignments
6.7
Linear Inequalities in Two Variables
Solve for y, if possible. Identify the slope and y-intercept. Graph.
1. y  2 x  6
2. 3x  2 y  12
y
3. y 
________
y
________
m  _______
m  _______
b  ________
b  ________
4. y  4 x  5
1
x 1
3
y
________
y
________
m  _______
m  _______
b  ________
b  ________
5. 4 x  2 y  6
6. 7  3x  y
y
________
y
________
m  _______
m  _______
b  ________
b  ________
MATH 0310 Homework Assignments
6.7
(Continued)
Solve for y, if possible. Identify the slope and y-intercept. Graph.
7. 5x  3 y  9
8. 2 y  7 x  8
y
________
y
________
m  _______
m  _______
b  ________
b  ________
9. 2 x  3 y
10. x  4 y  0
y
________
y
________
m  _______
m  _______
b  ________
b  ________
11. y  3
12. x  5
y
________
y
________
m  _______
m  _______
b  ________
b  ________
MATH 0310 Homework Assignments
Ch 7
7.3
Solving Quadratic Equations
Extraction of Roots Method and Completing the Square
Method
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Use the Extraction of Roots method to find the solutions of the following
quadratic equations.
1. x  25
2
8. 7 x  2  0
2. x  80
9. 2 x  3  8
3. x  121
10. (2 x  7)  6
4. x  64  0
11. (4 x  5)  9
5. 4 x  81  0
12. ( x  1)  75
2
2
2
2
6. 9 x  49  0
2
7. 5 x  8  0
2
2
2
2
2
13. (3x  5)  27
2
2
14. (5 x  1)  50
2
Find the solutions of the following quadratic equations by completing the
square.
15. x  4 x  1  0
20. 4 x  4 x  2  0
16. x  2 x  7  0
21. 2 x  5 x  4  0
17. x  4 x  29  0
22. 4 x  4 x  17  0
18. x  2 x  37  0
23. 4 x  12 x  7  0
2
2
2
2
19. x  5 x  2  0
2
2
2
2
2
MATH 0310 Homework Assignments
7.4
Quadratic Formula
Do all work on notebook paper. All steps should be shown. All work
should be neat and organized.
Use the quadratic formula to find the solutions of the following quadratic
equations.
1. x  9 x  9  0
8. 2 x  8 x  7  0
2. 9 x  2 x  2  0
9. 4 x  4 x  3  0
3. 8x  10 x  1  0
10. 8x  4 x  5  0
4. 6 x  2 x  5  0
11. x(2 x  3)  7
5. x  6 x  8  0
12. 2 x( x  3)  1
6. 8 x  x  2  0
13. ( x  5)(3x  1)  4
2
2
2
2
2
2
7. 4 x  6 x  9  0
2
2
2
2
14.
1 1 1
  0
2 x x2