Directions: Be sure to make an electronic copy of your answer before submitting it to Ashworth College for grading. Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be a minimum of one (1) single-spaced page to a maximum of two (2) pages in length; refer to the "Assignment Format" page for specific format requirements.

NOTE: Show your work on the problems.

1.Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y.

x|y| = x + 9

This is not a function. When x=3, there are two values of y, -4 and 4

2.Use the graph of the function to estimate:

a.f(2)= 6

b.f(–4)= 0

c.All x such that f(x) = 0

x=-4

3.For the following graph:

a.Find the domain of f.(-∞,∞)

b.Find the range of f.(-∞,4)

c.Find the x-intercepts.(-1,0),(3,0)

d.Find the y-intercept.(0,3)

e.Find the intervals over which f is increasing.(-∞,1)

f.Find the intervals over which f is decreasing.(1,∞)

g.Find the intervals over which f is constant.(1,4)

...ALGEBRA
In all three of these problems there is use of all of the terms required: simplify, like terms, coefficient, distribution, and removing parentheses. There is also use with the real number properties of the commutative property of addition and the commutative property of multiplication. In what ways are the properties of real numbers useful for simplifying algebraic expression? The properties are useful for identifying what should go where and with what, to make it simpler to understand and to solve the equation properly. When we break things down to a simplified process, it is much easier to see how the real numbers are placed and why they are placed that way. Real numbers do not actually show the value of something real in the “real world”. For example, in mathematics if we write 0.5 we mean exactly half, but in the real world half may not be exactly half. In all reality, we use mathematics every single day, whether we consciously realize it or not. Math is the key subject that applies to our everyday lives in the “real world”.
Expression number one like terms are combined by adding coefficients, the removal of parentheses, and the use of commutative property of addition and multiplication. Expression number two has the use of quite a bit of distribution, combining like terms, and removal of parentheses. Expression number three like terms are combined by adding coefficients also. In this expression there is a temporary addition of...

...Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis.
For historical reasons, the word "algebra" has several related meanings in mathematics, as a single word or with qualifiers.
• As a single word without article, "algebra" names a broad part of mathematics (see below).
• As a single word with article or in plural, "algebra" denotes a specific mathematical structure. Seealgebra (ring theory) and algebra over a field.
• With a qualifier, there is the same distinction:
• Without article, it means a part of algebra, like linear algebra, elementary algebra (the symbol-manipulation rules taught in elementary courses of mathematics as part of primary and secondary education), or abstract algebra (the study of the algebraic structures for themselves).
• With an article, it means an instance of some abstract structure, like a Lie algebra or an associative algebra.
• Frequently both meanings exist for the same qualifier, like in the sentence: Commutative algebra is the study of commutative rings, that all arecommutative algebras over the integers.
• Sometimes "algebra" is also used to denote the operations and methods related to algebra in the study of a structure that does not belong to...

...Accelerated Coordinate Algebra / Analytic Geometry Part A
Dr. Khan, Ph.D., Fall 2012
ekhan@marietta-city.k12.ga.us
WHY ARE YOU TAKING THIS COURSE?
All Georgia high school students are required to take four years of mathematics. Taking Accelerated Coordinate Algebra / Analytic Geometry Part A is comparable to taking the typical ninth grade course, Coordinate Algebra AND the first half of the tenth grade course, Analytic Geometry. The reason for acceleration of the first three courses is to provide ample room in a student’s schedule to incorporate higher level mathematics classes in future years.
WHAT WILL YOU LEARN?
Accelerated Coordinate Algebra / Analytic Geometry Part A covers topics in algebra, geometry, and statistics.
Unit 1: Relationships Between Quantities
Unit 2: Reasoning with Equations and Inequalities
Unit 3: Linear and Exponential Functions
Unit 4: Describing Data
Unit 5: Transformations in the Coordinate Plane
Unit 6: Connecting Algebra and Geometry Through Coordinates
Unit 7: Similarity, Congruence, and Proofs
Unit 8: Right Triangle Trigonometry
Unit 9: Circles and Volume
The first semester of Accelerated Coordinate Algebra / Analytic Geometry Part A will cover the first five units. Second semester will include the last four units. During the second semester students will take the End of Course Test in Coordinate...

...that there are many aspects of Algebra that the majority of people do not use on a daily basis. I think that this fact is what leads people to the false conclusion that Algebra is useless.
To better understand our topic, let’s define what we mean when we say “Algebra”. Webster’s dictionary defines Algebra as “a form of mathematics dealing with symbols and equations.” A guest in the mathematics forum on xpmath.com states that “…the truth is that Algebra is not much more than arithmetic expanded to the point where you don’t have to do trial and error to get an answer.” This guest goes on to explain that “…if you view it from that perspective, and overlook the outdated nature of some problems’ data, then you’ll recognize that indeed math deserves a place in your career; the more competent you can become with it, the better you’ll be able to competently manage you life.” I wholeheartedly agree with the preceding statement.
However, I’m not completely certain that math is THE MOST important subject we’ll ever learn; I believe that English quite important as well.
Math describes how everything in our environment works. A working knowledge of mathematics enables us to make accurate measurements and predictions. Since Algebra uses letters to represent numbers, it forces us to leap from concrete to abstract thinking. This “new thinking” method is, I believe, the reason Algebra...

...The CENTRE for EDUCATION in MATHEMATICS and COMPUTING
PATTERNING
AND
ALGEBRA: ALGEBRAIC EXPRESSIONS
This resource may be copied in its entirety, but is not to be used for commercial purposes without permission from the Centre for Education in Mathematics and Computing, University of Waterloo.
Play the Late Delivery game first! Levels 1 and 2 are recommended. Click on http://www.bbc.co.uk/education/mathsfile/shockwave/games/postie.html or go to www.wiredmath.ca for the link. 1. a. Write each of the following expression as a single number. i. 20 + 5 ii. 15 ÷ 3
iii. 11 × 9
b. For each question in (a) write 3 equivalent expressions using 3 different operations. 2. Match up the equivalent expressions below:
4+3 1+ 2 6×2+2 16 ÷ 2
55 − 52
2×2×2 49 ÷ 7 7×2
Did You Know?
A cheetah can run 76 km/h. The fastest human can only run about 37 km/h!
3.
The scale balances because the mass on the left side is equal to the mass on the right side. A number sentence can be written to describe the picture: 10 + 10 + 1 = 10 + 5 + 5 + 1 or 2 × 10 + 1 = 2 × 5 + 10 + 1 . a. Draw 3 different combinations of masses on a scale that would balance.
b. Write a number sentence to describe each of the 3 new combinations.
4.
a. Balance the scale using a combination of 10 g, 5 g and 1 g weights. Assume you have many different masses. Compare your solution with your classmates.
b. Write an equivalent expression, which is different than the masses...

...PROFICIENCY TEST STUDY GUIDE
With sample test questions
MATHEMATICS / ALGEBRA |
Key Words and Converting Words to EquationsFractions Adding, subtracting, multiplying, dividing Simplifying Writing decimals as fractions StatisticsReading Tables and ChartsExponentsPre-Algebra and Algebra Special notation for multiplication and division with variable Algebra word problems Order of operations Simplifying expressions Prime factorization Greatest common factor Least common multiple Factoring Sample algebra problemsCoordinate System Grid graph Slope coordinatesGeometry Basics Squares, rectangles, circles, trianglesMath Definitions |
ENGLISH |
Proof reading / spellingReading comprehensionMain theme of a paragraphLogical sequence of a paragraphKey wordEnglish grammarBasic word meanings |
ABILITY TO ASSIST |
Worker roles and responsibilitiesStudent discipline / behavior |
WRITING |
ContentFormatGrammarSpellingPunctuation |
MDUSD Proficiency Test Study Guide / Page 2
MATH
Key Words and Converting Words to Equations
Sometimes math questions use key words to indicate what operation to perform. Becoming familiar with these key words will help you determine what the question is asking for.
OPERATION | OTHER WORDS WHICH INDICATE THE OPERATION |
Addition | Increased by; more...

...make mathematics, especially the algebra as enjoyable as possible to those freshmen students in high school level and allow them to be productive as a student upon integrating the computer-assisted program in their studies.
Algebra is a branch of mathematics concerning the study of structure, relation, and quantity. Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. This only means that algebra needs thorough discussion on the part of the teacher and the assessment with its mathematical concepts to students in a language that they would understand (Dugolski, 2006).
A growing number of students are finding it difficult to make the conceptual leap from the concrete numbers of arithmetic to the abstract variables of algebra (Bach & Leither, 2006). A student finds it hard to incorporate their learned principles in their daily lives particularly as they have learned from school. The lack of personal encounter and connection of the basic principles of algebra in their daily living makes it more difficult on their part to really understand the concept of algebra.
Polynomials are the basic language of algebra. This deals with the use of the four fundamental operations. This is use in algebra to express and represent quantities in general, such as perimeter, area, revenue, and the...

...preferences and predilections. Those of the Islamic mathematician were toward numbers and algebra. Yet trigonometry and computation of tables cannot be omitted. One of the greatest contributors al-Khwarizmi, the often called `Father of Algebra.
Medieval Mathematics and Mathematicians
The medieval period was a period of gradual mathematical development. In other ways it was a period of great philosophical shifts, not so much on the surface as the Roman Church dominated much of philosophy and all of religion but underneath, the old Aristotelian views began to erode. Though it would dominate education for many more centuries, certain notions began to be be admitted. Most particularly, we see a lively discussion of the infinite, actual and potential.
The rise of the mercantile class required mathematical training, if only for finance. A subculture of mathematicians were needed to train the sons of the wealthy merchants.
Renaissance Mathematics and Mathematicians
Following the medieval period, mathematics begins to make formidable advances in the 15th century. Mercantile forces demanded the creation of an exceptionally wealthy class of individuals. To sustain such wealth required an infrastructure that required mathematical education as an important component.
The first country to be impacted were the Italians. Unhampered by previous eras of mathematical prohibitions, they freely entered the world of algebra, imprinting it with...