Intro to Domain, Range, and Functions.

Relation
The relationship between
sets of information from
with a set of starting
points called domain and
ending points called range.

Relation
Domain Range
x y
0 1

1 2

2 3

3 4

4 5

{(0,1),(1,2),(2,3),(3,4),(4,5)}

Domain
The x-values of the
ordered pairs.
x y
Domain
0 1 0
1 2 1
2 3 2
3 4 3
4
4 5

Range
The y-values of the
ordered pairs.
x y
Range
0 1 1
1 2 2
2 3 3
3 4 4
5
4 5

1. What the is domain?
{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}
A. {-3,6,-1,6,3}
B. {2,4,3,6,2}
C. {2,3,4,6}
D. {-3,-1,3,6}

2. Write the domain as a set.
(4,3) (-1,4) (6,7)
(5,2) (-2,1) (3,9)
A. {4,-1,6,5,-2,3}
B. {-2,-1,3,4,5,6}
C. {1,2,3,4,7,9}
D. {-2,-1,2,3,4,5}

3.With the relation, the y-values
are considered

A. Range
B. Ending points
C. Starting points
D. A and B

4. What is the relation with the
corresponding range?
{-9,-2,1,4,5}
A. {(1,5),(3,1),(1,-2),(4,-9),(1,4)}
B. {(5,2),(1,1),(-2,3),(-9,1),(4,4)}
C. {(3,9),(5,8),(-9,1),(-2,4),(5,-2)}
D. {(5,3),(-2,4),(1,1),(-9,1),(4,4)}

5.When looking for the domain,
you are really looking for the
y-values of the relation.
A. True
B. False

6. What is the range?
{(-1,2),(3,2)}

A. {-1,3}
B. {2}

Function
This is considered a
“well-behaved” relation.

Function
If you find a duplicate x-
value, then you do not have
a function

Function
Domain Range
0
1
1
2
These are functions.
2 3 There are only one x
3 4
4 5 for every y, even if
Domain
3
Range
there are is two x’s for
6 0
one y. Focus on the x’s.
1
8 3

2 1

Function
Domain Range
0
1
1
2
These are not
2 3 functions. Two x’s for
3 4
4 5 one y. Unacceptable.
Domain
7
Range
9
An x without even a y?
4 0 Very unacceptable.
0 3
1 4
2

To be a function or to not be?

Graph

7. For a relation to be a
function, you cannot
A. have duplicate x-values.
B. have duplicate y-values.

8. Is this a function?
(4,3) (-1,4) (6,7)
(5,2) (-2,1) (3,9)
A. No
B. Yes

9. Why is this a function?
(4,3) (-1,4) (6,2)
(5,2) (-2,1) (3,9)
A. {1,2,3,4,9}
B. {-2,-1,3,4,5,6}
C. {-2,1,3,4,5,6}
D. A and B.

Intro to Domain, Range, and Functions.

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