Precalculus Relations and Functions

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. 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.

• Model data with both single and multivariable functions

• Visualize and analyze data using different technologies.

• Understand properties of different types of functions to apply them accordingly to model different situations.

• Perform vector operations, such as addition, scalar multiplication, dot product, and cross product, to analyze geometry in space.

Syllabus

Syllabus - What you will learn from this course
Week 1
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.
Week 2
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.
Week 3
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.
Week 4
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.

FAQ

When will I have access to the lectures and assignments?

Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:

What will I get if I subscribe to this Specialization?

When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

Is financial aid available?

Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

Reviews

It will be nice to see more applications of the the material.

Thoughtful and clear explanations. Advice on an associated textbook would be helpful.

Great course explained everything concisely. However the sample problems and test of week 1 had certain sums which were not covered in the video

Excellent course. The professor made it easier to understand the material.