1. Relations Objectives The student will be able to:
1. identify the domain and range of a relation.
2. show relations as sets and mappings.

2. 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.

3. How about some more definitions? The domain is the
set of 1st coordinates of the ordered pairs.
The range is the
set of 2nd coordinates of the ordered pairs.
A relation is a
set of ordered pairs.

4. 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:
Range:
*If a number occurs more than once, you do not need to list it more than one time.

5. Given the relation {(3,2), (1,6), (-2,0)}, find the domain and range.

6. Practice: Find the domain and range of the following sets of ordered pairs.
1. {(3,7),(-3,7),(7,-2),(-8,-5),(0,-1)}
Domain:{3,-3,7,-8,0}
Range:{7,-2,-5,-1}

7. What would this be? {(2,4), (3,-1), (0,-4)}
A bad relationship!! Ha! Ha!

8. The relation {(2,1), (-1,3), (0,4)} can be shown byx y
1) a table.
2) a mapping.
3) a graph. 2 -1 1 3 4 2 -1 1 3 4

9. Relation = {(-1,3), (0,6), (4,-1), (7,3)}
Given the following table, show the relation, domain, range, and mapping. x y
Relation = {(-1,3), (0,6), (4,-1), (7,3)}
Domain = {-1, 0, 4, 7}
Range = {3, 6, -1,}

10. You do not need to write 3 twice in the range!
Mapping x y -1 4 7 3 6 -1
You do not need to write 3 twice in the range!

11. What is the domain of the relation {(2,1), (4,2), (3,3), (4,1)}
{2, 3, 4, 4}
{1, 2, 3, 1}
{2, 3, 4}
{1, 2, 3}
{1, 2, 3, 4}
Answer Now

12. What is the range of the relation {(2,1), (4,2), (3,3), (4,1)}
{2, 3, 4, 4}
{1, 2, 3, 1}
{2, 3, 4}
{1, 2, 3}
{1, 2, 3, 4}
Answer Now

13. 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}

14. Find the Domain and Range of the Following Sets of Ordered Pairs #’s 1, 4
{(3,7),(-3,7),(7,-2),(-8,-5)} 3. 4.
D: {-8,-3,3,7} R: {-5,-2,7}
D: {All Reals} R: {y > -4}
D: {x: x 0} R: {y: y 0}
D: {x: x > 3} R: {All Reals}

15. Objectives The student will be able to:
1. To determine if a relation is a function.
2. To find the value of a function.
SOL: A.7aef
Designed by Skip Tyler, Varina High School

16. 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).
f(x) y x

17. Function Notation
Input
Name of Function
Output

18. Determine whether each relation is a function.
1. {(2, 3), (3, 0), (5, 2), (4, 3)}
YES, every domain is different!
f(x) 2 3
f(x) 3
f(x) 5 2
f(x) 4 3

19. Determine whether the relation is a function.
2. {(4, 1), (5, 2), (5, 3), (6, 6), (1, 9)}
f(x) 4 1
f(x) 5 2
NO, 5 is paired with 2 numbers!
f(x) 5 3
f(x) 6
f(x) 1 9

20. Is this relation a function? {(1,3), (2,3), (3,3)}
Yes No
Answer Now

21. 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!

22. Vertical Line Test
FUNCTION!
NO!
NO WAY!
FUNCTION!

23. Is this a graph of a function?
Yes No
Answer Now

24. 3(3)-2 3 7 -2 -8 3(-2)-2 Given f(x) = 3x - 2, find: 1) f(3) = 7
= -8
3(-2)-2 -2 -8

25. Given h(z) = z2 - 4z + 9, find h(-3)
(-3)2-4(-3)+9 -3 30
h(-3) = 30

26. Given g(x) = x2 – 2, find g(4) 2 6 14 18
Answer Now

27. Given f(x) = 2x + 1, find -4[f(3) – f(1)]
-40
-16 -8 4
Answer Now