Grade 11- Concept of functions rev.1.pptx

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This document defines key terms related to functions such as domain, range, and piecewise functions. It provides examples of representing functions using tables, ordered pairs, graphs, and equations. It also discusses how to determine if a relation represents a function and describes piecewise functions as using more than one formula with separate domains.

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Grade 11- Concept of functions rev.1.pptx

1. Define functions and related terms;
2. Determine if the given relation represent a function;
3. Define piecewise function; and
4. represent real life situations using functions, including
piece wise functions.

It is the set of first coordinates.
a. Range
b. Domain
c. Abscissa

It is a set of second coordinates
a. Range
b. Domain
c. Abscissa

Find the domain and range of the given ordered pairs.
{(1, -1), (2, -3),(0, 5), (-1, 3), (4,-5), (-1, 5), (4, -4)}
Domain- {-1, 0, 1, 2, 4}
Range- {-5, -4, -3, -1, 3, 5}

is any set of ordered pairs. The set of all first elements of the
ordered pairs is called the domain of the relation, and the set of
all second elements is called the range. Members of these sets
are called elements.
A relation from set A to set B is defined to be any subset
of A x B. if R is a relation from A to B and (a, b) ∈ R, then we
say that “a is related to b” and it is denoted as a R b.

Functions- is a correspondence between two sets
where each element in the domain, corresponds to
exactly one element in range.
Functions can represent in four ways.
1. A table of values
Example:
2. Ordered pairs
Example: {(-2, 10), (-1, -7), (0, -4), (1, -1), (2, 2)}

3. Graph, and
Example:
4. Equation
Example: y= 3x-4

Determine if the following relations are functions or
not function?
f= { (1, 2), (2, 2), (3, 5), (4, 5)}
g= { ( 1, 3), (1, 4), (2, 5) ( 2, 6), (3, 7)}
h= { ( 1, 3), (2, 6), ( 3, 9), …, (n, 3n),… }

Determine whether the relationship given in the
mapping diagram is a function or not a function.

Vertical Lines
A graph represent a function if and only if each
vertical line intersects the graph at the most once.

Which of the following equation describe a function?

-Display the inputs and corresponding outputs of a
function. Function Tables can be vertical (up and
down) or horizontal (Side to side)

Below is the example of a function table of A(r)=𝜋𝑟2
r A(r)=𝜋𝑟2
0.5
1.0
1.5
2.0
2.5
0.79
3.14
7.07
19.63
12.57

Evaluate, prepare a
function table and
graph
f(x)= x+1 if:
a) f (-2)
b) f (-1)
c) f (0)
d) f 1
e) f (2)
X x+1
-2
-1
0
1
2
-1
0
1
3
2

Evaluate, prepare a
function table and
graph
f(x)= 3𝑥2
+x-5 if:
a) f(-2)
b) f(0)
c) f(4)
d) f
1
2
x 3𝑥2+x-5
-2
0
4
𝟏
𝟐
5
-5
47
−15
4

Evaluate, prepare a
function table and
graph
f(x)= 𝑥2
if:
a) f (-2)
b) f (-1)
c) f (0)
d) f 1
e) f (2)
r A(r)=𝜋𝑟2
-2
-1
0
1
2
4
1
0
4
1

-is a function in which more than one formula is used
to define the output. Each formula has its own
domain, and the domain of the function is the
union of all these smaller domains.

Evaluate f (x) when a) x=0, b) x=2 and c) x=4
f (x) = x+2 if x<2
2x+1 if x ≥ 2

Graph the following equation
f (x) = 2x-5 if x<-2
𝑥2
-3 if x ≥ −2

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This PowerPoint presentation is based on Unit 7 – Assisting Individuals and Families to Promote and Maintain Their Health, a core topic in Community Health Nursing – I for 5th Semester B.Sc Nursing students, as per the Indian Nursing Council (INC) guidelines. The unit emphasizes the nurse’s role in family-centered care, early detection of health problems, health promotion, and appropriate referrals, especially in the context of home visits and community outreach. It also strengthens the student’s understanding of nursing responsibilities in real-life community settings. 📘 Key Topics Covered in the Presentation: Introduction to family health care: needs, principles, and objectives Assessment of health needs of individuals, families, and groups Observation and documentation during home visits and field assessments Identifying risk factors: environmental, behavioral, genetic, and social Conducting growth and development monitoring in infants and children Recording and observing: Milestones of development Menstrual health and reproductive cycle Temperature, blood pressure, and vital signs General physical appearance and personal hygiene Social assessment: understanding family dynamics, occupation, income, living conditions Health education and counseling for individuals and families Guidelines for early detection and referral of communicable and non-communicable diseases Maintenance of family health records and individual health cards Assisting families with: Maternal and child care Elderly and chronic disease management Hygiene and nutrition guidance Utilization of community resources – referral linkages, support services, and local health programs Role of nurse in coordinating care, advocating for vulnerable individuals, and empowering families Promoting self-care and family participation in disease prevention and health maintenance This presentation is highly useful for: Nursing students preparing for internal exams, university theory papers, or community postings Health educators conducting family teaching sessions Students conducting fieldwork and project work during community postings Public health nurses and outreach workers dealing with preventive, promotive, and rehabilitative care It’s structured in a step-by-step format, featuring tables, case examples, and simplified explanations tailored for easy understanding and classroom delivery.

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Assisting Individuals and Families to Promote and Maintain Health – Unit 7 | ...RAKESH SAJJAN

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Grade 11- Concept of functions rev.1.pptx

2. 1. Define functions and related terms; 2. Determine if the given relation represent a function; 3. Define piecewise function; and 4. represent real life situations using functions, including piece wise functions.

4. It is the set of first coordinates. a. Range b. Domain c. Abscissa

5. It is a set of second coordinates a. Range b. Domain c. Abscissa

6. Find the domain and range of the given ordered pairs. {(1, -1), (2, -3),(0, 5), (-1, 3), (4,-5), (-1, 5), (4, -4)} Domain- {-1, 0, 1, 2, 4} Range- {-5, -4, -3, -1, 3, 5}

8. is any set of ordered pairs. The set of all first elements of the ordered pairs is called the domain of the relation, and the set of all second elements is called the range. Members of these sets are called elements. A relation from set A to set B is defined to be any subset of A x B. if R is a relation from A to B and (a, b) ∈ R, then we say that “a is related to b” and it is denoted as a R b.

9. A B

10. Functions- is a correspondence between two sets where each element in the domain, corresponds to exactly one element in range. Functions can represent in four ways. 1. A table of values Example: 2. Ordered pairs Example: {(-2, 10), (-1, -7), (0, -4), (1, -1), (2, 2)}

11. 3. Graph, and Example: 4. Equation Example: y= 3x-4

12. Determine if the following relations are functions or not function? f= { (1, 2), (2, 2), (3, 5), (4, 5)} g= { ( 1, 3), (1, 4), (2, 5) ( 2, 6), (3, 7)} h= { ( 1, 3), (2, 6), ( 3, 9), …, (n, 3n),… }

13. Determine whether the relationship given in the mapping diagram is a function or not a function.

14. Determine whether the relationship given in the mapping diagram is a function or not a function.

15. Vertical Lines A graph represent a function if and only if each vertical line intersects the graph at the most once.

16. Vertical Lines A graph represent a function if and only if each vertical line intersects the graph at the most once.

17. Which of the following equation describe a function?

18. -Display the inputs and corresponding outputs of a function. Function Tables can be vertical (up and down) or horizontal (Side to side)

19. Below is the example of a function table of A(r)=𝜋𝑟2 r A(r)=𝜋𝑟2 0.5 1.0 1.5 2.0 2.5 0.79 3.14 7.07 19.63 12.57

20. Evaluate, prepare a function table and graph f(x)= x+1 if: a) f (-2) b) f (-1) c) f (0) d) f 1 e) f (2) X x+1 -2 -1 0 1 2 -1 0 1 3 2

21. Evaluate, prepare a function table and graph f(x)= 3𝑥2 +x-5 if: a) f(-2) b) f(0) c) f(4) d) f 1 2 x 3𝑥2+x-5 -2 0 4 𝟏 𝟐 5 -5 47 −15 4

22. Evaluate, prepare a function table and graph f(x)= 𝑥2 if: a) f (-2) b) f (-1) c) f (0) d) f 1 e) f (2) r A(r)=𝜋𝑟2 -2 -1 0 1 2 4 1 0 4 1

23. -is a function in which more than one formula is used to define the output. Each formula has its own domain, and the domain of the function is the union of all these smaller domains.

24. Evaluate f (x) when a) x=0, b) x=2 and c) x=4 f (x) = x+2 if x<2 2x+1 if x ≥ 2

25. Graph the following equation f (x) = 2x-5 if x<-2 𝑥2 -3 if x ≥ −2

Editor's Notes

#9: If x and y are elements of these sets and if a relation exist between x and y, then we say that x corresponds to y depends on x. We may represent it as the ordered pair (x, y)
#10: Question Are the pictures in column A related to column B? How? Column A is a set that contains the different body parts used to sense objects in column B. The rule is to match the body part in A correctly to an object in B.
#12: If x and y are elements of these sets and if a relation exist between x and y, then we say that x corresponds to y depends on x. We may represent it as the ordered pair (x, y)

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Grade 11- Concept of functions rev.1.pptx

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Editor's Notes