Lesson 1: Functions and Relations Flashcards
Set of x values
Domain
Set of y values
Range
Ordered pairs
(x,y)
A rule that relates the values from a set of values (called the domain) to a second set of values (called the range).
Relations
In relations, inputs generate:
one or more outputs
A relation where each element in the domain is related to only one value in the range by some rule
Function
In functions, inputs generate:
only one output
A function is a set of ordered pairs where:
no ordered pairs have the same x value
between two sets X and Y is simply a subset of the Cartesian product X x Y, i.e., a collection of ordered pairs (x,y) where x ∈ X and y ∈ Y
Relation
∈ means
“is an element of”
Let x and Y be sets. Then a function from X to Y, denoted by f: X -> Y, is a set f of ordered pairs in X x Y such that for each x ∈ X there exists a unique y ∈ Y with (x,y) ∈ f. In other words, if (x,y) ∈ f and (x,y’) ∈ f, then y=y’
Function
Function Notation
f(x)
f(x) is read as
“f of x” or “function of x”
in f(x)=y, what are the variables?
- x is the independent variable
- y is the dependent variable
A function can be illustrated as:
a machine where there is an input and output
