Functions are the bedrock of mathematical equations and expressions. Without them, mathematical operations involving addition, subtraction, multiplication, and division would not be of much use. They are also crucial to the comparisons made between groupings of integers and groupings of real numbers. Although relations are similar to functions in mathematics, they are more involved with elements as a subset of the Cartesian product. Database administrators will find aspects of functions and relations discussed in this course useful in relational database management systems like MySQL and IBM Db2. For instance, data from tables wrongly pulled out of parent tables is closely related to topics discussed in this course. Also, challenges involving 1-to-1, 1-to-many, and many-to-many relations are explained at fundamental mathematical levels.

Relations can often be confused with functions. Want to know the distinction between them? Complete this course and understand the simple solution to this common mistake. You will also be able to answer long-debated questions involving important concepts surrounding functions and relations. One such question is: Are all functions relations and, if they aren’t, can two lists disagree on the properties of an element? Answers to questions like these are included to help you learn about mathematical sets and elements. You will learn how to correctly compare input and output elements among sets. Learners will evaluate sample problems that are necessary to ground them in rational, polynomial, exponential, and logarithmic functions. Sample problems are solved in an easy step-by-step manner while showcasing the best ways to end up at the desired solutions.

Pre-calculus has a long history in the development of scientific theories involving relationships between physical, chemical, and even imaginary quantities. Today, we are surrounded by products of pre-calculus including the building you either are in right now or the one you just stepped out of. Without pre-calculus, engineers would not be able to find the exact length of electricity cables required to connect the substation from where you get your electricity. The beautiful architectural structures we admire all over the world are products of pre-calculus involving geometry, graphing, and algebra - all of which are explained in this course from foundational to advanced levels. You will learn to solve pre-calculus problems from start to finish, and see how to evaluate the properties for various functions and conic sections.