Four Ways to Represent a Function (part 1)
MAT 135: Calculus
1 Sept 2009
Basic question
Given two quantities that relate to each other,
how do we phrase that relationship precisely?
A function f is a rule
that assigns to each element x in a set D
exactly one element called f(x) in a set E
FUNCTIONS
A function is a RULE
http://xkcd.com/183
A precise, unambiguous set of 
directions for doing something
Accepts INPUT
x : Input = INDEPENDENT VARIABLE
D : Set of computable inputs = DOMAIN
Produces UNIQUE OUTPUT
f(x) : Output = VALUE of f at x, DEPENDENT VARIABLE
E: Set of outputs that can be produced = RANGE
*** Only one output per input
GRAPHS
TABLES
FORMULAS
VERBAL DESCRIPTIONS
Domain = [-2,5)
Range = [-1,2]
V(0) = ____;  V(3) = ___; V(5) = ___
Values for which V(t) = 0?
Domain = (-∞, ∞) or R (set of all real numbers)
Range = (0,0.85]
y(0) = ____;  y(5) = ____
Domain = {0, 1, 2,..., 800} 
Range = {F, D-, D, ..., A-, A}
G(522) = D
G(722) = A-
Save for Thursday :)
Assignment
Read through syllabus
Read Section 1.1., esp. examples
Watch email for further info on web site, online homework
Work as many textbook exercises as you can
Link to this presentation:
http://prezi.com/160743