Functions & Graphs — Introduction
Calculus is the mathematics that describes and investigates rates of change which, fundamentally, is going to rely on a deep understanding of functions. More generally, it requires an understanding of data which allows a mathematical analysis of said data.
In this initial chapter on Functions and Graphs, we will begin by defining the functions necessary to study calculus — polynomial, rational, trigonometric, exponential, and logarithmic functions. We will review how to evaluate these functions, as well as explore the properties of their graphs.
Provide examples of equations with terms involving these functions. Illustrate algebraic techniques necessary to solve them. Foundation for material to come. Essential to be familiar and comfortable with these ideas before moving forwards to the formal intro of calculus in the next chapter.
Notes
Major earthquakes have occurred around the world in several countries in last few years. In Jan 2010 a magnitude 7.3 earthquake hit Haiti. In March 2011 a magnitude 9 obliterated northeastern Japan. In April 2014 an 8.2-magnitude struck off Chilean coast. [1] What do these numbers mean? How does a magnitude 9 compare to an 8.2 or a 7.3? We will cover later in this chapter how we use logarithmic functions to compare relative intensity of two earthquakes based on magnitude. [1]
Resources
- Calculus I. Openstax.