## Exam 1 Study Guide

• Chapter 1
• basic algebra
• functions
• f(x) notation
• domain
• range
• even and odd functions
• increasing and decreasing functions
• composite functions, f o g.
• one-to-one functions and inverse functions, f-1
• graphs
• the definition
• transformations (translations, stretching and shrinking, ...)
• particular types of functions
• polynomials
• rational functions
• trig functions
• power functions : ax.
• The definition of e and the exponential function ex.
• logarithms, loga x, and the natural logarithm, ln x.
• |x|
• Chapter 2
• slope of a line
• secant line, average rate of change over an interval, average velocity
• tangent line, instantaneous rate of change, instantaneous velocity
• limits, continuity, differentiability
• horizontal and vertical asymptotes
• the derivative function
• derivatives of simple functions directly from the definition, such as:
• 1
• x
• x2
• x3
• sqrt x
• 1/(sqrt x)
• 1/x
• ...
• sums, multiples and transformations of the functions above