Relation Slides.ppt data structure slides for explained process

Relation Slides. data structure slides for explained process

1. Relations & Functions
The relation can be described as
 a collection of
ordered pairs. It is used to relate an object from one
set to the other set, and the sets must be non-empty.
The relation can contain two or more than two sets.
Muhammad Mohsin Saeed

2. Introduction to Functions
Warm Up
State whether each word or phrase represents an
amount that is increasing, decreasing, or constant.

1. Stays the same Constant
2. Rises Increase
3. Drops Decrease
4. Slows down Decrease

3. The air temperature increased steadily for several hours
and then remained constant. At the end of the day, the
temperature increased slightly before dropping sharply.
Choose the graph that best represents this situation.
Read the graphs from left to right to show time passing .
Example

4. Sketching Graphs for Situations
Sketch a graph for the situation. Tell whether the graph
is continuous or discrete.
A small bookstore sold
between 5 and 8 books
each day for 7 days. The
number of books sold
(y-axis) varies for each
day (x-axis). Since the
bookstore accounts for
the number of books
sold at the end of each
day, the graph is 7
distinct points.
The graph is discrete.

5. You have seen relationships represented by graphs.
Relationships can also be represented by a set of
ordered pairs called a relation.
Relations
In the scoring systems of some track meets, for first
place you get 5 points, for second place you get 3 points,
for third place you get 2 points, and for fourth place you
get 1 point. This scoring system is a relation, so it can be
shown by ordered pairs. {(1, 5), (2, 3), (3, 2) (4, 1)}. You
can also show relations in other ways, such as tables,
graphs, or mapping diagrams.

6. Graphs can be used to illustrate many different
situations. For example, trends shown on a
cardiograph can help a doctor see how a patient’s
heart is functioning.
Key Concept of Graph

7. Relations & Functions
Evaluating functions
Remember, the DOMAIN is the set of INPUT values
and the RANGE is the set of OUTPUT values.
y = 3x + 4
inputoutput

8. 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.
Another way to remember them is…

9. Key Point

10. Given the relation
{(3,2), (1,6), (-2,0)},
find the domain and range.
Domain = {3, 1, -2}
Range = {2, 6, 0}

11. The relation {(2,1), (-1,3), (0,4)}
can be shown by either……
1) a table.
2) a mapping.
3) a graph.
x y
2
-1
0
1
3
4
2
-1
0
1
3
4

12. Given the following table, show the
relation, domain, range, and mapping.
x-1047
y36-13
Relation = {(-1,3), (0,6), (4,-1), (7,3)}
Domain = {-1, 0, 4, 7}
Range = {3, 6, -1, 3}

13. Mapping
x-1047
y36-13
You do not need to write 3 twice in the range!
-1
0
4
7
3
6
-1

14. What is the domain of the relation
{(2,1), (4,2), (3,3), (4,1)}
1.{2, 3, 4, 4}
2.{1, 2, 3, 1}
3.{2, 3, 4}
4.{1, 2, 3}
5.{1, 2, 3, 4}
Answer Now

15. What is the range of the relation
{(2,1), (4,2), (3,3), (4,1)}
1.{2, 3, 4, 4}
2.{1, 2, 3, 1}
3.{2, 3, 4}
4.{1, 2, 3}
5.{1, 2, 3, 4}
Answer Now

16. Inverse of a Relation: For every
ordered pair (x,y) there must be a (y,x).
Write the relation and the inverse.
Relation = {(-1,-6), (3,-4), (3,2), (4,2)}
Inverse = {(-6,-1), (-4,3), (2,3), (2,4)}
-1
3
4
-6
-4
2

17. Write the inverse of the mapping.
1.{(4,-3),(2,-3),(3,-3),(-1,-3)}
2.{(-3,4),(-3,3),(-3,-1),(-3,2)}
3.{-3}
4.{-1, 2, 3, 4}
-3
4
3
-1
2
Answer Now

18. 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)x y

19. Function Notation
Output
Input
Name of
Function
yfx

20. 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 0
f(x)
5 2
f(x)
4 3

21. 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
f(x)
5 3
f(x)
6 6
f(x)
1 9
NO,
5 is paired with 2 numbers!

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

23. 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!

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

25. Is this a graph of a function?
1.Yes
2.No
Answer Now

26. Given f(x) = 3x - 2, find:
1) f(3)
2) f(-2)
3(3)-23 7
3(-2)-2-2 -8
= 7
= -8

27. Given h(z) = z
2
- 4z + 9, find z(-3)
(-3)
2
-4(-3)+9-3 30
9 + 12 + 9
h(-3) = 30

28. Given g(x) = x
2
– 2, find g(4)
1.2
2.6
3.14
4.18
Answer Now