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Algebra

Elementary to Advanced - Functions & Applications

Joseph W. Cutrone, PhD

After completing this course, students will learn how to successfully apply functions to model different data and real world occurrences. This course reviews the concept of a function and then provide multiple examples of common and uncommon types of functions used in a variety of disciplines. Formulas, domains, ranges, graphs, intercepts, and fundamental behavior are all analyzed using both algebraic and analytic techniques. From this core set of functions, new functions are created by arithmetic operations and function composition. These functions are then applied to solve real world problems. The ability to picture many different types of functions will help students learn how and when to apply these functions, as well as give students the geometric intuition to understand the algebraic techniques. The skills and objectives from this course improve problem solving abilities.

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What's inside

Syllabus

Module 1: Introduction to Functions

A linear relationship between two variables occurs when there is a constant increase or constant decrease in one variable with respect to the other. Linear functions have the property that any chance in the independent variable results in a proportional change in the dependent variable. Many physical situations can be modeled using a linear relationship. Adding an extra term of the form ax^2 to a linear function creates a quadratic function, and its graph is the parabola. We will see examples of linear and quadratic functions and their applications in the sections that follow.

Module 2: Other Common Functions

In the last module we introduced the important concept of a function and considered the linear and quadratic functions. In this module, we discuss methods for building new functions from those that are already familiar to use. One method will use the graph shifting techniques already introduced. These methods are developed further and applied to new functions. Constructing a graph is often an important first step in solving a problem. The more functions you can picture, the better problem solver you will be.

Final Exam: Functions and Applications

Congratulations on reaching the final exam! This final assessment will be cumulative in nature, covering all aspects of the course. Use this final as a teaching tool: justify what you know and identify areas for improvement. Use scrap paper as you take this final. Try to use any formula sheets or outside resources as a tool and not a crutch. Check your answers before you submit. After the test, review any incorrect answers to find your mistakes. Try to separate "silly" mistakes from the more substantial mistakes in understanding. Good luck!

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Builds a foundation for understanding graphical representation of functions

Implements graphical techniques to solve real world problems

Develops problem solving abilities

Develops skills for applying functions to model data and real world occurrences

Applicable to various disciplines

Introduces common and uncommon types of functions

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Reviews summary

Excellent elementary and advanced algebra refresher

Learners say that this is a nearly perfect online course for reviewing elementary to advanced algebra. Well-taught videos, helpful readings, and challenging assessments were noted. The course covers functions, applications, quadratic equations, and more. Most students said the amount of content was sufficient but a few students mentioned wanting more advanced challenges. Overall, this course may be perfect for you if you're looking for a quick and engaging refresher on the basics of algebra.

Engaging assessments test practical applications

"Excellent course materials and instruction videos. Also, I found that the questions of quizzes and exams are highly innovative. They are not meant for testing mere theoretical knowledge, but also, test one's ability to think apply the theoretical knowledge gained"

"This course was very good and also very challenging. The videos do present the information and the reading assignments have the necessary information needed. The test seem to be on another level given the problemsand the values used. revealed how much I had forgotten when it came to solving the algebra and advanced algebraic functions"

"Straightforward until it hits the module on quadratic functions - urgh! I had to do a lot of independent reading in order to understand terms and processes that were mentioned but never described (e.g., factoring and foiling). Still, I guess that's what learning is all about and I got there in the end. A workout but worth it"

Provides solid overview of functions and applications

"Excellent course. I've done 2/3 of the specialization and looking forward to course #3"

"This was a brilliant experience for second times,. Gradually my Algebraic skills are improving amazingly and these courses makes me more enthusiastic about the charm of algebra"

"It is a brief, compact class of Precalculus (Relations and Functions) from the same Online Instructor in Coursera. It gives more emphasis in the derivation and solving of a mathematical model by using Elementary Algebra and Calculus-based techniques"

Well-organized, presented, and engaging

"Clear and concise"

"Very nice refresher"

"Course is well organized and orchestrated"

Taught by skilled instructor

"Excellent "

"Great instructor, exercises, and explanations"

"The teacher is a pro at explaining"

May be too challenging for beginners but helpful for those with some background

"VERY INFORMATIVE AND WELL PRESENTED ADVANCED ALGEBRA COURSE"

"This is for understanding fundamental in algebra function and application and also extremely helpful for preparing for university studies "

Consider adding more practice questions and videos for certain difficult topics

"Pleas make more questions to practice that are similar to the questions on the quizes and final. The second week needs a video to explain how to apply the equations to the word probles given on the quizies and final"

"good. but with frequent lacunae. stuff doesn't get comprehensively explained and/or demonstrated"

"This was a brilliant experience for second times,. Gradually my Algebraic skills are improving amazingly and these courses makes me more enthusiastic about the charm of algebra"

Activities

Coming soon We're preparing activities for Algebra: Elementary to Advanced - Functions & Applications. These are activities you can do either before, during, or after a course.

Career center

Learners who complete Algebra: Elementary to Advanced - Functions & Applications will develop knowledge and skills that may be useful to these careers:

Statistician

Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data. They use algebra to understand the underlying principles of statistics, and to develop models to analyze data. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for statisticians to be successful in their careers.

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Data Scientist

Data scientists use data to solve business problems. They use mathematical and statistical techniques to analyze data, and to develop models and algorithms to predict future outcomes. Algebra is essential for data scientists to understand the underlying principles of data analysis, and to develop models and algorithms that are accurate and reliable. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for data scientists to be successful in their careers.

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Software Engineer

Software engineers use mathematical and statistical techniques to develop software. They use algebra to understand the underlying principles of software engineering, and to develop algorithms and data structures. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for software engineers to be successful in their careers.

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Financial Analyst

Financial analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. They use algebra to understand the underlying principles of finance, and to develop models to assess risk and return. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for financial analysts to be successful in their careers.

See salaries and explore the career path for Financial Analyst

Product Manager

Product managers use mathematical and statistical techniques to develop and launch new products. They use algebra to understand the underlying principles of product management, and to develop models to analyze market data and make product decisions. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for product managers to be successful in their careers.

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Operations Manager

Operations managers use mathematical and statistical techniques to manage business operations. They use algebra to understand the underlying principles of operations management, and to develop models to optimize systems and processes. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for operations managers to be successful in their careers.

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Actuary

Actuaries use mathematical and statistical skills to assess risk and uncertainty. They apply this knowledge to problems in insurance, finance, and other fields. Algebra is essential for actuaries to understand the underlying principles of risk and uncertainty, and to develop models to assess and manage risk. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for actuaries to be successful in their careers.

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Investment Banker

Investment bankers use mathematical and statistical techniques to analyze financial data and make investment recommendations. They use algebra to understand the underlying principles of finance, and to develop models to assess risk and return. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for investment bankers to be successful in their careers.

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Risk Manager

Risk managers use mathematical and statistical techniques to assess risk and uncertainty. They use algebra to understand the underlying principles of risk management, and to develop models to assess and manage risk. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for risk managers to be successful in their careers.

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Financial Planner

Financial planners use mathematical and statistical techniques to help clients plan for their financial future. They use algebra to understand the underlying principles of finance, and to develop financial plans for clients. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for financial planners to be successful in their careers.

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Economist

Economists use mathematical and statistical techniques to analyze economic data and make policy recommendations. They use algebra to understand the underlying principles of economics, and to develop models to analyze economic data. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for economists to be successful in their careers.

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Market Researcher

Market researchers use mathematical and statistical techniques to analyze market data and make recommendations. They use algebra to understand the underlying principles of market research, and to develop models to predict consumer behavior. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for market researchers to be successful in their careers.

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Quantitative Analyst

Quantitative analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. They use algebra to understand the underlying principles of finance, and to develop models to assess risk and return. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for quantitative analysts to be successful in their careers.

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Operations Research Analyst

Operations research analysts use mathematical and statistical techniques to solve problems in business and industry. They use algebra to understand the underlying principles of operations research, and to develop models to optimize systems and processes. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for operations research analysts to be successful in their careers.

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Teacher

Teachers use mathematical and statistical techniques to teach students about math and statistics. They use algebra to understand the underlying principles of math and statistics, and to develop lesson plans and activities to teach students. This course provides a solid foundation in algebra, including the study of functions and their applications. This knowledge is essential for teachers to be successful in their careers.

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Reading list

We've selected 14 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in Algebra: Elementary to Advanced - Functions & Applications.

Calculus: Early Transcendentals, Student Solutions...

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Provides a comprehensive introduction to the concepts of calculus. It is particularly useful for students who are planning to take further courses in mathematics or who need to use calculus in their work.

Calculus: Early Transcendentals Single Variable,...

Kindle Edition

$$$

Calculus: Early Transcendentals, Student Solutions...

Kindle Edition

$$$

Calculus Early Transcendentals Single Variable,...

Paperback

$$$$

Student Solutions Manual to accompany Calculus...

Paperback

$$$

Algebra and Trigonometry

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Provides a comprehensive review of the mathematical concepts and skills that are necessary for success in calculus. It is especially useful for students who are planning to take calculus or who need to brush up on their math skills.

Algebra

Elementary to Advanced - Functions & Applications

What's inside

Syllabus

Good to know

Save this course

Reviews summary

Excellent elementary and advanced algebra refresher

Activities

Career center

Reading list

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