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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!

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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

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Algebra: Elementary to Advanced - Functions & Applications with these activities:

Find a mentor who can help you with functions

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Having a mentor can help you learn about functions and improve your skills.

Browse courses on Functions

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Identify potential mentors within your personal and professional networks
Reach out to potential mentors and inquire about their willingness to provide guidance.
Discuss your goals and expectations with your mentor

Read and summarize the book 'Algebra and Trigonometry' by John H. Saxon, Jr.

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Read the book to deepen your understanding of functions.

View Melania on Amazon

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Purchase the book
Set a goal for when you will complete the book
Break the book into smaller chunks

Compile a list of websites that offer practice problems on functions

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Compiling a list of websites that offer practice problems on functions.

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Search for websites that offer practice problems on functions
Create a list of the websites
Share the list with other students

Three other activities

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Solve equations involving linear and quadratic functions

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Solve equations involving linear and quadratic functions.

Browse courses on Linear Functions

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Identify the type of function
Apply the appropriate algebraic techniques
Check your answer

Graph functions

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Graphing functions can help you visualize their behavior and understand their properties.

Browse courses on Linear Functions

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Plot the points
Connect the points
Label the axes

Create a poster on the different types of functions

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Create a poster outlining different types of functions and their applications.

Browse courses on Functions

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Research different types of functions
Design the poster
Print the poster

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.

See salaries and explore the career path for Statistician

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.

See salaries and explore the career path for Data Scientist

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.

See salaries and explore the career path for Software Engineer

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.

See salaries and explore the career path for Product Manager

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.

See salaries and explore the career path for Operations Manager

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.

See salaries and explore the career path for Actuary

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.

See salaries and explore the career path for Investment Banker

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.

See salaries and explore the career path for Risk Manager

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.

See salaries and explore the career path for Financial Planner

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.

See salaries and explore the career path for Economist

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.

See salaries and explore the career path for Market Researcher

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.

See salaries and explore the career path for Quantitative Analyst

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.

See salaries and explore the career path for Operations Research Analyst

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.

See salaries and explore the career path for Teacher

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

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Algebra

Elementary to Advanced - Functions & Applications

Two deals to help you save

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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