Precalculus: Relations and Functions

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