Download 2.1 Notes on Domain and Range

2.1 Domain and Range of
Functions
Vocabulary
●
●
●
●
Relation – A relation is a general term
for any set of ordered pairs.
Function – A function is a special type
of relation in which each member of the
domain is paired with exactly one
member of the range.
Domain – The domain is the set of all
x-coordinates in a set of ordered pairs.
Range – The range is the set of all
y-coordinates in a set of ordered pairs.
Name the Domain and Range
The following set of ordered pairs has a
limited number of points.
Ex:{(2,3),(-1,0),(2,-5),(0,-3)}
Domain:  1, 0, 2 
Range:
5,  3, 0, 3
*If a number occurs more than once, you do
not need to list it more than one time.
Name the Domain and Range
From a Graph
The set of ordered
pairs may be an
infinite number of
points as described
by a graph.
Domain:{all real numbers}
Range:{y:y≥0}
Find the Domain and Range
The set of ordered pairs may be an infinite number of points
as described by an equation.
Find the domain and range of y 
x5
What limits do we have for x? x - 5 must be a positive value
so x – 5 > 0.
What limits do we have for y? Square roots are always
positive.
Domain:
Range:
 x : x  5
 y : y  0
Functions

A function is a relation in which each
element of the domain is paired with
exactly one element of the range.
Another way of saying it is that there is
one and only one output (y) with each
input (x).
x
f(x)
y
Function Notation
y  f x 
Input
Output
Name of
Function
Determine whether the
relation is a function.
{(2, 3), (3, 0), (5, 2), (4, 3)}
2
3
5
4
f(x)
f(x)
f(x)
f(x)
3
0
2
3
YES, every domain is different!
Determine whether the relation
is a function.
{(4, 1), (5, 2), (5, 3), (6, 6)}
4
5
5
6
f(x)
f(x)
f(x)
f(x)
1
2
3
6
NO,
5 is paired with 2
numbers!
Is this relation a function?
{(1,3), (2,3), (3,3)}
1.
2.
Yes
No
Answer Now
Vertical Line Test (pencil test)


If any vertical line passes through more than
one point of the graph, then that relation is
not a function.
Are these functions?
FUNCTION!
FUNCTION!
NOPE!
Vertical Line Test
FUNCTION!
NO!
NO WAY!
FUNCTION!
Is this a graph of a function?
1.
2.
Yes
No
Answer Now
Given f(x) = 3x - 2, find:
 1) f(3)= 7
3

3(3)-2
7
= -8
2) f(-2)
-2
3(-2)-2
-8
Given h(z) = z2 - 4z + 9, find h(-3)
-3
2
(-3) -4(-3)+9
9 + 12 + 9
h(-3) = 30
30
Given g(x) = x2 – 2, find g(-4)
1.
2.
3.
4.
2
6
14
18
Answer Now
Given f(x) = 2x + 1, find
-4[f(3) – f(1)]
1.
2.
3.
4.
-40
-16
-8
4
Answer Now
Find the Domain and Range of the
Following Sets of Ordered Pairs
1. {(3,7),(-3,7),(7,-2),(-8,-5)}
D: {-8,-3,3,7}
R: {-5,-2,7}
2.
D: {x: x > 3}
R: {All Reals}
3.
f ( x)  3x 2  4
4.
2
f ( x) 
x
D: {All Reals} R: {y > -4}
D: {x: x  0}
R: {y: y  0}