Relation and function.pdf learnongjknfjn

PRE
PRE
ASSESSMENT
ASSESSMENT
GENERAL MATHEMATICS
JUNE 23,2025

PRAYER
LEADER: LET US PAUSE FOR A MOMENT AND PLACE OURSELVES IN
THE PRESENCE OF GOD.
ALL: IN THE NAME OF THE FATHER, AND OF THE SON, AND OF
THE HOLY SPIRIT. AMEN.
L: OUR FATHER, WHO ART IN HEAVEN, HALLOWED BE THY NAME.
THY KINGDOM COME, THY WILL BE DONE, ON EARTH AS IT IS IN
HEAVEN.
R: GIVE US THIS DAY OUR DAILY BREAD. AND FORGIVE US OUR
TRESPASSES, AS WE FORGIVE THOSE WHO TRESPASS AGAINST US.
AND LEAD US NOT INTO TEMPTATION, BUT DELIVER US FROM
EVIL.
AMEN.

1.What is a relation?
A. A comparison of numbers
B. A set of ordered pairs
C. A graph of inequalities
D. A function rule

2. Function is a special kind of
relation where:
A. Inputs can repeat
B. Each input has exactly one output
C.Outputs can’t repeat
D. Each output has only one input

3. The domain is:
A. The set of outputs
B. The rule of the function
C. The set of inputs
D. The x-values multiplied

4.The range is:
A. The set of all outputs
B. The x-values
C. A type of graph
D. The rule of a function

5.Which is an example of a function?
A. {(1, 2), (2, 3), (1, 4)}
B. {(1, 2), (2, 3), (3, 4)}
C. {(2, 5), (2, 5), (2, 5)}
D. {(4, 6), (5, 6), (4, 6)}

6.What is an ordered pair?
A. A number set
B. A pair of rules
C. A pairing of inputs and outputs
D. Two formulas

7.Which is NOT part of a function?
A. Domain
B. Rule
C. Equation
D. Repeating inputs with different
outputs

8.What makes a relation not a
function?
A. Repeating outputs
B. Inputs matching only one
output
C. One input with two outputs
D. Negative values

9.What is a mapping diagram used for?
A. Drawing graphs
B. Showing inequalities
C. Showing how inputs are paired with
outputs
D. Measuring data

10.Which set is a function?
A. {(a, 1), (a, 2)}
B. {(b, 1), (c, 1)}
C. {(1, a), (1, b)}
D. {(x, 1), (x, 3)}

11.One-to-One means:
A. Each input has the same output
B. Each output is shared
C. Each input maps to a unique output
D. All outputs are used

12. Many-to-One means:
A. All inputs are the same
B. Multiple inputs have the same
output
C. Each output has many inputs
D. Inputs repeat

13.Onto means:
A. No inputs repeat
B. Every codomain element has a
mapping
C. Some outputs are unused
D. Function has two rules

14. Into means:
A. No inputs repeat
B. Every codomain element has a mapping
C. Some outputs are unused
D. Function has two rules

15.What makes a mapping not a
function?
A. One input going to two outputs
B. Different inputs going to the
same output
C. Outputs that are the same
D. Inputs that repeat

16. {(1, A), (2, A), (3, B)} is:
A. One-to-One
B. Not a function
C. Many-to-One
D. Into

17.A function where no output
is left unused is:
A. Onto
B. Into
C. One-to-One
D. Many-to-One

18.{(A, 1), (B, 2), (C, 3)} is:
A. Many-to-One
B. Into
C. One-to-One and Onto
D. Not a function

19.Mapping with more
codomain values than
used is:
A. Onto
B. Into
C. Not a function
D. One-to-One

20.If two different
inputs map to the same
output, the function is:
A. Not a function
B. One-to-One
C. Many-to-One
D. Into

RELATION
RELATION
AND
AND
FUNCTION
FUNCTION
GENERAL MATHEMATICS
JUNE 23,2025

PICTURE
PICTURE
ANALYSIS
ANALYSIS
GENERAL MATHEMATICS
JUNE 23,2025

JUNE 24,2025
FIREMAN
1. Why is it important to identify the roles of
one’s person in the community?
2. How does the role of one’s person in the
community affect their behevior towards the
other persons?

FUNCTION
FUNCTION
or
or NOT
NOT ?
?

Students stand up and move to the side they
believe is correct.
Ask for volunteers to explain their choice.
Clarify the answer, review the concept briefly,
and move to the next round.

{(2, 4), (3, 5), (2, 6)}
or
or
1
1
Which of the relation a
function?
{(1, 3), (2, 4), (3, 5)}

1
1 Is the relation a function?
{(1, 3), (2, 4), (3, 5)}

X
2
3
2
or
or
Y
4
5
6
2
2 X
1
2
3
Y
A

x Y
5 11
6 12
5 11
3
3
or
or
x Y
1 3
2 6
3 9

A graph passes the
vertical line test (no
vertical line intersects
the graph in more than
one point).
on the curve.
A graph where
one vertical
line intersects
two points
4
4
or
or

A graph passes the
vertical line test (no
vertical line intersects
the graph in more than
one point).
on the curve.
4
4

A person's name
and their
cellphone
numbers (one
person has two
phone numbers)
5
5
or
or
The number of
siblings a
student has
(input: student,
output: number
of siblings).

5
5 The number of
siblings a
student has
(input: student,
output: number
of siblings).

RELATION is any set of ordered pairs
from one set (called the domain) are
associated with elements in another set
(called the codomain or range).

EXAMPLE
Give the domain and range of the
following:
1.((1,3),(2,4),(5,6),(6,8))
2.((-2,4),(-1,1),(2,0),(1,5),(2,-2))

RELATION in which each member of the
domain is paired to exactly one
member of the range is called a
function.

Which of the following relations are
function?
1.A=((1,3),(2,4),(5,6),(6,8))
2.B=((2,2),(1,1),(3,3),(4,4),(5,5))
3.C=((0,1),(1,0),(-1,0),(-1,0))
4.D=((-2,4),(-1,1),(0,0),(1,1),(2,4))

FUNCTION can also be represented
through mapping. In this case the
relation or function is represented by
the set of all the connections by the
arrows

Which of the following the function.
Function Not Function Function
Note:If any input value is mapped to more than one output value, the
diagram does not represent a function.

Function as a graph in the cartesian plane.
Give the graph of a relation, we can easily identify
if it is a function or not by using vertical line test.
A graph of a mathematical relationis said to be a
function if any vertical line drawn passing through
the graph touches the graph at exactly one point.

Which of the following graphs represent a function?
Note:If any input value is mapped to more than one output value, the
diagram does not represent a function.

is simply to ‘plug and chug’. it means insertung
a certain value for the variable x( the plug) to
get the result of y(the chug)
Example:
1.Evaluate the function f(x)=2x=4 for x=5.
2.If f(x)=x²+3x-2, find f(-3).
Evaluating
Functions

Example:
1.If g(x)=3x²-5x, find g(2).
2.If h(x)= 6x-3, find h(4).
7
3. If f(x)=16x³+4x-2, find f(½).
Evaluating Functions

Definition: A function f:A→B is
one-one or injective if every
element of the domain maps to
a unique element in the
codomain.
Condition: If f(a1)=f(a2) ⇒a1=a2.
Example: f(x)=2x one-one for
real numbers.
One-One
Function
(Injective)

Types of Functions Based on Mapping
One-One Function (Injective)
Onto Function (Surjective)
One-One Onto Function (Bijective)
Many-One Function
Into Function

Definition: A function f:A→B is onto or
surjective if every element of the
codomain has at least one pre-image
in the domain.
Condition: For every b∈B, there
exists at least one a∈Asuch that
f(a)=b
Example: : f(x) = x^3 is onto for real
numbers, as every real number is the
cube of some real number.
Onto
Function
(Surjective)

Definition: A function is bijective if
it is both one-one and onto.
Properties:
1.Every element of the codomain is
mapped by exactly one element of
the domain.
2.Bijective functions are invertible.
Example: f(x)=x+1is bijective for real
numbers.
One-One
Onto
Function
(Bijective)

Definition: A function f:A→Bis
many-one if two or more
elements in the domain map to
the same element in the
codomain.
Example:f(x) = x^2 is many-one
for real numbers since
f(2)=f(−2)=4
Many-One
Function

Definition: A function f:A→B is into
if there is at least one element in
the codomain that is not mapped
by any element of the domain.
Example: If f:{1,2}→{a,b,c} and
f(1)=a, f(2)=b, then c is not mapped
—so the function is into.
Into
Function

INSTRUCTION
Draw a sample mapping diagram for
each type.
Use sets A = {1, 2, 3} and B = {a, b, c,
d}

_____________ can be classified based on
mapping—how elements from one set
(called the _________) are associated with
elements in another set (called the
__________).

What are the Types of Functions Based
on Mapping?

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