Week 2: Functions of one variable and their graphs, shifting of graphs

Thomas Calculus, Early Transcedentals (13th edition)

Chapter 1 Functions

Functions are fundamental to the study of calculus. In this chapter we review what functions are and how they are pictured as graphs, how they are combined and transformed, and ways they can be classified. We review the trigonometric functions, and we discuss misrepresentations that can occur when using calculators and computers to obtain a function’s graph. We also discuss inverse, exponential, and logarithmic functions. The real number system, Cartesian coordinates, straight lines, circles, parabolas, and ellipses are reviewed in the Appendices.

Sec 1.1 Functions and Their Graphs (pages: 1 - 13)

Functions are a tool for describing the real world in mathematical terms. A function can be represented by an equation, a graph, a numerical table, or a verbal description; we will use all four representations throughout this book. This section reviews these function ideas.

Sec 1.2 Combining Functions: Shifting and Scaling Graphs (pages: 14 - 20)

In this section we look at the main ways functions are combined or transformed to form new functions.