We’ve already practiced creating new functions by translating and stretching the graphs of parent functions. In this module, we’ll explore even more ways to build new functions from existing ones. We'll begin by looking at how two functions can be combined to create a new one. Then, we’ll move on to explore inverse functions. Throughout the rest of the course, we’ll keep using these ideas to understand and work with different types of functions.

In this module, we explore two new types of functions that arise when modeling natural phenomena: exponential and logarithmic functions. For example, exponential functions are used to represent the growth of a population, the value of an investment, and the elimination of a drug from the body. Logarithmic functions are the inverses of exponential functions. We will start by examining the key features of these functions and their graphs, then look at algebraic rules to transform and solve equations with them. Finally, we will apply exponential and logarithmic functions to build models and make predictions.

For the last module of this course, we will explore rational functions, which arise naturally when modeling inverse variation. These functions are defined as quotients of polynomials. We will learn about the domain, range, and graphs of rational functions, and practice manipulating them with algebra. Finally, we will see how to solve rational equations.