Function

Definition

dependence relationship

one dependent value for each independent value

 

Representations

verbal

numeric (table)

graphic (graph of pair of values)

algebraic (equation)

Notation

Domain and Range

Sign Analysis (check for 0 in both numerator & denominator of rational functions)

Discrete and Continuous

Piecewise

Absolute Value (write as piecewise)

Vertical Line Test
 

Operations on functions

Sums, Differences, Products & Quotients of functions

Composition

Translations

Reflections

 

Symmetry

Even and Odd functions
 

Velocity as a slope of s= f(t)
 

Trigonometric functions

Polynomial functions

Rational functions

Vertical asymptotes

Horizontal asymptotes

holes vs. asymptotes

Inverse functions

Notation

Interpretation from context

(There are other types of functions, i.e. exponential, logarithmic, etc. we’ll see some of these later)

 

Outline of Topics : Chapter 2

2-sided limit / 1-sided limit

Numeric approach

Graphic approach

Algebraic approach

limits of polynomials

x -> a

x -> infinity (elephant & goldfish)

limits of rational functions

x -> a

x -> infinity (elephant & goldfish)

limits of piecewise functions

limits of trigonometric functions
 

definition

removable discontinuity