Transcript Relations and Functions

Relations and Functions
1-1 and 1-2
Unit 1
English Casbarro
Definitions
Ordered Pair- a pair of numbers which has an
input value and an output value
Relation- a collection of ordered pairs
Domain- the set of all of the input values
Range- the set of all of the output values
Function- a relation where every input value is
matched with a single output value
Representations of Relations
Mapping
Coordinate Plane
1
6
2
4
3
2
Set Notation:
{(2,4), (5,4), (6,7), (4,1)}
A table of values:
Is this Relation a Function?
Remember that a function must have a different output value for
each input value.
Is this relation a function?
Is this relation a function?
 Since every x-value on a vertical line
is the same number, then it is NOT a
function.
 Vertical Line Test– if a vertical line
crosses a graph, and passes through
the graph more than once, the graph
is NOT a function.
Turn in the following
problem
Warm-up
Write the definitions of the following
terms:
1. set2. ordered pairs3. relationAre the following relations functions?
4. {(1,2), (2, 3), (1,5), (4,7)} yes no
5. {(1,4), (2,4), (7,5), (5, 8)} yes no
1-2: Function Notation
 When the relation is determined to be
a function, and you can write a rule
to describe it, it is written in function
notation.
Example 1: Evaluating functions
Knowing what this means:
Be careful that you are saying:
f(x) means f of x, or the output
value of the function f at the input
value x.
So, f(5) means the output value of the
function f at the input value 5.
Dependent and Independent
Variables
The “y” value is said to be the dependent variable because it depends on the
value that is chosen for the “x” variable. In this example, d(t) depends on the
value that you choose for t. So, d(t) is the dependent variable and t is the
Independent variable.
Now, you try:
Turn in the following
problems