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