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 : a
^{x}
.
The definition of e and the exponential function e
^{x}
.
logarithms, log
_{a}
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
x
^{2}
x
^{3}
sqrt x
1/(sqrt x)
1/x
...
sums, multiples and transformations of the functions above