Precalculus: Relations and Functions (Coursera)

Precalculus: Relations and Functions (Coursera)

This course helps to build the foundational material to use mathematics as a tool to model, understand, and interpret the world around us. This is done through studying functions, their properties, and applications to data analysis. Concepts of precalculus provide the set of tools for the beginning student to begin their scientific career, preparing them for future science and calculus courses. This course is designed for all students, not just those interested in further mathematics courses.

Class Deals by MOOC List - Click here and see Coursera's Active Discounts, Deals, and Promo Codes.

Students interested in the natural sciences, computer sciences, psychology, sociology, or similar will genuinely benefit from this introductory course, applying the skills learned to their discipline to analyze and interpret their subject material. Students will be presented with not only new ideas, but also new applications of an old subject. Real-life data, exercise sets, and regular assessments help to motivate and reinforce the content in this course, leading to learning and mastery.

Course 1 of 3 in the Precalculus through Data and Modelling Specialization

Syllabus

WEEK 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.

WEEK 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.

WEEK 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.

WEEK 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.

Go to Class
MOOC List is learner-supported. When you buy through links on our site, we may earn an affiliate commission.

Related Courses

Business Applications of Hypothesis Testing and Confidence Interval Estimation (Coursera) Coursera
Rice University

Business Applications of Hypothesis Testing and Confidence Interval Estimation (Coursera)

Confidence intervals and Hypothesis tests are very important tools in the Business Statistics toolbox. A mastery over these topics will help enhance your business decision making and allow you to understand and measure the extent of ‘risk’ or ‘uncertainty’ in various business processes. This course advances your knowledge about Business Statistics by introducing you to Confidence Intervals and Hypothesis Testing. These are done by easy to understand applications.

Aug 10th 2026
4 Weeks
Introduction to Mathematical Thinking (Coursera) Coursera
Stanford University

Introduction to Mathematical Thinking (Coursera)

Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself.

Aug 10th 2026
5-12 Weeks
Functional Programming in Scala Capstone (Coursera) Coursera
École Polytechnique Fédérale de Lausanne

Functional Programming in Scala Capstone (Coursera)

In the final capstone project you will apply the skills you learned by building a large data-intensive application using real-world data. You will implement a complete application processing several gigabytes of data. This application will show interactive visualizations of the evolution of temperatures over time all over the world.

Aug 10th 2026
5-12 Weeks
Data science perspectives on pandemic management (Coursera) Coursera
Politecnico di Milano

Data science perspectives on pandemic management (Coursera)

The COVID-19 pandemic is one of the first world-wide scenarios where data made a difference in capturing and analyzing the diffusion and impact of the disease. We offer an introductory course for decision makers, policy makers, public bodies, NGOs, and private organizations about methods, tools, and experiences on the use of data for managing current and future pandemic scenarios.

Aug 10th 2026
5-12 Weeks
Data intelligence for businesses and managers (Coursera) Coursera
Institut Mines-Telecom

Data intelligence for businesses and managers (Coursera)

With the proliferation of connected objects (computers, tablets, watches, etc.), huge masses of data are generated every second. This Big Data has led to the emergence of a data economy, where data is the main source of competitive advantage for companies. In this sense, data and its processing tools have become a strategic priority for companies, and the main gas pedal of their digital transformation.

Aug 10th 2026
5-12 Weeks
Healthcare Information Design and Visualizations (Coursera) Coursera
Northeastern University

Healthcare Information Design and Visualizations (Coursera)

Introduces processes and design principles for creating meaningful displays of information that support effective business decision-making. Studies how to collect and process data; create visualizations (both static and interactive); and use them to provide insight into a problem, situation, or opportunity. Introduces methods to critique visualizations along with ways to answer the elusive question: “What makes a visualization effective?”

Aug 10th 2026
4 Weeks
Visualization for Data Journalism (Coursera) Coursera
University of Illinois at Urbana-Champaign

Visualization for Data Journalism (Coursera)

While telling stories with data has been part of the news practice since its earliest days, it is in the midst of a renaissance. Graphics desks which used to be deemed as “the art department,” a subfield outside the work of newsrooms, are becoming a core part of newsrooms’ operation. Those people (they often have various titles: data journalists, news artists, graphic reporters, developers, etc.) who design news graphics are expected to be full-fledged journalists and work closely with reporters and editors.

Aug 10th 2026
5-12 Weeks
Introduction à la théorie de Galois (Coursera) Coursera
École normale supérieure

Introduction à la théorie de Galois (Coursera)

Le cours expose la théorie de Galois, du classique critère de non-résolubilité des équations polynomiales aux méthodes plus avancées de calcul de groupes de Galois par réduction modulo un nombre premier. Le thème général de cette théorie est l'étude des racines d'un polynôme et concerne en particulier la possibilité de les exprimer à partir des coefficients de ce polynôme. Evariste Galois considère les symétries de ces racines et associe ainsi à ce polynôme un groupe de permutations de ses racines, que l'on appelle maintenant son groupe de Galois.

Aug 3rd 2026
5-12 Weeks
Calculus: Single Variable Part 2 - Differentiation (Coursera) Coursera
University of Pennsylvania

Calculus: Single Variable Part 2 - Differentiation (Coursera)

Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.

Aug 3rd 2026
3 Weeks
Initiation à la théorie des distributions (Coursera) Coursera
École Polytechnique

Initiation à la théorie des distributions (Coursera)

Une fonction discontinue peut-elle être solution d'une équation différentielle? Comment définir rigoureusement la masse de Dirac (une "fonction" d'intégrale un, nulle partout sauf en un point) et ses dérivées? Peut-on définir une notion de "dérivée d'ordre fractionnaire"? Cette initiation aux distributions répond à ces questions - et à bien d'autres.

Aug 10th 2026
5-12 Weeks
Differential Equations Part III Systems of Equations (Coursera) Coursera
Korea Advanced Institute of Science and Technology - KAIST

Differential Equations Part III Systems of Equations (Coursera)

This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications.

Aug 10th 2026
5-12 Weeks