Precalculus: Relations and Functions from Coursera

What's inside

Syllabus

Module 1: Basics and Common Functions

Functions help to study the relationship between two or more variables. They are the basic quantitative tool used to visualize, analyze, and interpret these relationships. Studying functions is the first step in developing analytics skills for mathematical modeling. In this module, we develop the concept of a function and review important algebraic operations on functions used later in this course. We will also study the important features, like domain, range, and end behavior of graphs.

Module 2: Equations of Lines, Quadratics, and More Functions

In this module, we will study two common types of functions: linear and quadratic. We will learn how to identify common features of their graphs, and see how they can be used to model real world situations, particularly those involving revenue and cost. We will also further explore function compositions, and learn how to find the inverse of a function.

Module 3: Exponential and Logarithmic Functions

In this module, we expand our catalog of functions to study two new functions that arise when modelling natural phenomena: the exponential and logarithmic functions. In the last module, we saw that one-to-one functions have inverses, which reverse the function process. For example, the function f(x) = x^3 has as its inverse the function g(x) = x^(1/3). We now want to expand this process to find inverses for exponential functions - those of the form f(x) = a^x, where a is a positive number not equal to one.

Module 4: Properties of Logarithms

Understanding the logarithm as an exponent allows for important algebraic properties of the logarithm. In this module, we will explore these properties and their uses as we apply logarithms to real world examples.

Good to know

Know what's good

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Suitable for students planning careers in natural or computer sciences, psychology, sociology, or similar fields

Appropriate for learners with no prior experience in higher mathematics

Builds a strong foundation for further scientific or calculus courses

Applies mathematical concepts to analyze data and interpret real-world problems in various disciplines

Utilizes multiple learning resources, including real-life data, exercise sets, and assessments, to promote understanding and retention

Reviews summary

Precalculus with functions and relations

Learners say this Precalculus: Relations and Functions course is engaging, well-organized, and useful for reviewing or learning precalculus fundamentals. The lectures are clear, concise, and give examples. Quizzes and exercises are thought-provoking and help assess understanding. Students appreciate the explanations of algebraic concepts and applications to real-world problems. Overall, learners recommend this course for brush-ups or deeper dives into precalculus topics.

Focuses on precalculus basics

"For what it covers, this course is pretty good. Note that "relations and functions" is not at all the entirety of a Pre-Calculus course, so if you're looking for a full course, this is not it."

Well-explained lectures

"The lectures are clearer than any math teacher I ever had in school."

"The lectures were great and the assignments and quizzes were challenging."

Exercises and quizzes test understanding

"The difficulty of the quizzes is just right, enough to reinforce the concepts presented in the video lectures."

Engaging and well-organized

"The course was really nice and engaging, the videos were crystal clear and well made."

May be too slow for some

"I would definitely go through these lectures at a slow pace unless you already know all this material."

External textbook helpful

"Advice on an associated textbook would be helpful."

Some prior knowledge assumed

"This course is for people with some experience in precalculus."

Lack of feedback on quizzes

"In this course, all of that feedback is missing. When you get an answer wrong on a quiz, you don't see a solution worked out to help you figure out why you got it wrong."

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 Precalculus: Relations and Functions with these activities:

Algebra Review Exercises

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Practice algebra skills to strengthen your foundation.

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Solve equations
Simplify expressions
Graph linear functions

Review Precalculus Textbook

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Review the textbook before taking the course to refresh your memory on relevant concepts.

View Calculus for the AP® Course on Amazon

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Read through the chapter summaries
Complete the practice problems at the end of each chapter
Take notes on the main concepts

Khan Academy Precalculus Tutorials

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Follow video tutorials to reinforce your understanding of precalculus concepts.

Browse courses on Functions

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Watch the videos on the basics of functions
Complete the practice exercises
Take the quizzes to test your understanding

Four other activities

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Study Group Discussions

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Engage in discussions with peers to clarify concepts and solve problems together.

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Form a study group with classmates
Meet regularly to discuss course material
Work together on problem sets and assignments

Function Graphing Practice

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Practice graphing functions to improve your visualization and analysis skills.

Browse courses on Functions

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Plot points for a given function
Identify the domain and range of the function
Sketch the graph of the function

Exponential and Logarithmic Function Practice

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Practice working with exponential and logarithmic functions to enhance your problem-solving skills.

Browse courses on Exponential Functions

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Simplify exponential expressions
Solve exponential equations
Convert between exponential and logarithmic form

Function Modeling Project

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Apply your knowledge of functions to model a real-world phenomenon.

Browse courses on Functions

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Choose a phenomenon to model
Collect data on the phenomenon
Develop a mathematical function to represent the data
Evaluate the accuracy of the model

Career center

Learners who complete Precalculus: Relations and Functions will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists use scientific methods, algorithms, and systems to extract knowledge and insights from data in various forms, both structured and unstructured. Taking the Precalculus: Relations and Functions course can help you build a strong foundation for success in this field. The course provides a comprehensive understanding of functions, their properties, and applications to data analysis. This knowledge is essential for Data Scientists who need to analyze and interpret large datasets effectively.

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Statistician

Statisticians collect, analyze, interpret, and present data to help businesses and organizations make informed decisions. As a Statistician, you would need a strong foundation in mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in data analysis. This knowledge will be beneficial for your career as a Statistician.

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Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make recommendations on investments. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in financial analysis. This knowledge will be beneficial for your career as a Financial Analyst.

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Actuary

Actuaries use mathematical and statistical techniques to assess risk and uncertainty in various fields, including insurance, finance, and healthcare. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in actuarial science. This knowledge will be beneficial for your career as an Actuary.

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Economist

Economists use mathematical and statistical techniques to analyze economic data and make recommendations on economic policy. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in economics. This knowledge will be beneficial for your career as an Economist.

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Market Researcher

Market Researchers collect, analyze, and interpret data to understand consumer behavior and market trends. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in market research. This knowledge will be beneficial for your career as a Market Researcher.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to analyze complex systems and make recommendations for improvement. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in operations research. This knowledge will be beneficial for your career as an Operations Research Analyst.

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Business Analyst

Business Analysts use data analysis and problem-solving skills to improve business processes and make recommendations for change. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in business analysis. This knowledge will be beneficial for your career as a Business Analyst.

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Software Engineer

Software Engineers design, develop, and maintain software applications. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in software engineering. This knowledge will be beneficial for your career as a Software Engineer.

See salaries and explore the career path for Software Engineer

Data Analyst

Data Analysts collect, clean, and analyze data to find trends and patterns. They need a strong understanding of mathematics, including statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in data analysis. This knowledge will be beneficial for your career as a Data Analyst.

See salaries and explore the career path for Data Analyst

Computer Scientist

Computer Scientists design, develop, and implement computer systems. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in computer science. This knowledge will be beneficial for your career as a Computer Scientist.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical techniques to analyze financial data and make recommendations on investments. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in quantitative analysis. This knowledge will be beneficial for your career as a Quantitative Analyst.

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Risk Analyst

Risk Analysts use mathematical and statistical techniques to assess risk and uncertainty in various fields, including insurance, finance, and healthcare. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in risk analysis. This knowledge will be beneficial for your career as a Risk Analyst.

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Mathematician

Mathematicians develop new mathematical theories and solve mathematical problems. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in mathematics. This knowledge will be beneficial for your career as a Mathematician.

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Teacher

Teachers educate students in various subjects, including mathematics. They need a strong understanding of mathematics, including calculus and statistics. The Precalculus: Relations and Functions course provides a solid foundation for understanding the concepts of functions and their applications in teaching. This knowledge will be beneficial for your career as a Teacher.

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