1.1 Functions Given By Formulas
Functions
A function is a rule that assigns to each element of a set B exactly one element of some other
set A.
• each input (whatever that input may be) is assigned to exactly one output
• the set of all valid inputs is called the domain while the set of all outputs produced by
the function is called the range
•
f:D®C
range set (outputs)
function name domain set (inputs)
Example 1
Are the following correspondences functions? If not, explain why.
(a) (1,3) (2,5) (1,5) (3,6)
(b) (1,2) (3,4) (5,6) (7,8)
(c) (5,0) (-1,3) (5,6) (-2,9)
Function Notation
output =f input
( )
or more traditionally,
y=f x
( )
Example 2
Use function notation to represent the functions from example 1.
