General Mathematics - Representation and Types of FunctionsJuan Miguel Palero
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about the representation, definition, and types of functions.
General Mathematics - Representation and Types of FunctionsJuan Miguel Palero
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about the representation, definition, and types of functions.
The Sum of Two Functions
The Difference of Two functions
The Product of Two Functions
The Quotient of Two Functions
The Product of A constant and a Function
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
The Sum of Two Functions
The Difference of Two functions
The Product of Two Functions
The Quotient of Two Functions
The Product of A constant and a Function
It is a powerpoint presentation that will help the students to enrich their knowledge about Senior High School subject of General Mathematics. It is comprised about Rational functions and its zeroes. It is also comprised of some examples and exercises to be done for the said topic.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Embracing GenAI - A Strategic ImperativePeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
BÀI TẬP BỔ TRỢ TIẾNG ANH GLOBAL SUCCESS LỚP 3 - CẢ NĂM (CÓ FILE NGHE VÀ ĐÁP Á...
Relations and functions power point
1. Unit 4 - Relations and Functions 1
Relations and Functions
MGSE8.F.1 Understand that a function is a rule that assigns to each
input exactly one output. The graph of a function is the set of ordered
pairs consisting of an input and the corresponding output.
MGSE8.F.2 Compare properties of two functions each represented in
a different way (algebraically, graphically, numerically in tables, or by
verbal descriptions). For example, given a linear function represented
by a table of values and a linear function represented by an algebraic
expression, determine which function has the greater rate of change.
2. Essential
Questions:
Unit 4 - Relations and Functions 2
• What is a function?
• What are the characteristics of a function?
• How do you determine if a relation is a function?
• How is a function different from a relation?
• Why is it important to know which variable is the
independent variable?
3. Unit 4 - Relations and Functions 3
Some Definitions-
A relation between two variables x and y is a
set of ordered pairs
An ordered pair consists of an x and y-
coordinate
A relation may be viewed as ordered pairs,
mapping design, table, equation, or written in
sentences
x-values are input, independent variable,
domain.
y-values are output, dependent variable,
range
4. Unit 4 - Relations and Functions 4
Example 1:
What makes this a relation?
{( , ),( , ),( , ),( , ),( , ),( , )}
0 5 1 4 2 3 3 2 4 1 5 0
•What is the domain?
{0, 1, 2, 3, 4, 5}
What is the range?
{-5, -4, -3, -2, -1, 0}
5. Unit 4 - Relations and Functions 5
Example 2 –
Is this a relation?
•What is the domain?
{4, -5, 0, 9, -1}
•What is the range?
{-2, 7}
Input 4 –5 0 9 –1
–2 7
Output
6. Unit 4 - Relations and Functions
6
Is a relation a function?
What is a function?
According to a textbook, “a
function is…a relation in which
every input has exactly one
output”
7. Unit 4 - Relations and Functions 7
Is a relation a function?
•Focus on the x-coordinates, when given a relation
If the set of ordered pairs has different x-coordinates,
it ISA function
If the set of ordered pairs has same x-coordinates,
it is NOT a function
•Y-coordinates have no bearing in determining
functions
8. Unit 4 - Relations and Functions 8
Example 3
{( , ),( , ),( , ),( , ),( , ),( , )}
0 5 1 4 2 3 3 2 4 1 5 0
•Is this a relation?
•Is this a function?
•Hint: Look only at the x-coordinates
YES
YES
9. Unit 4 - Relations and Functions 9
Example 4
{(– , ),( , ),( , ),( , ),( , ),(– , )}
1 7 1 0 2 3 0 8 0 5 2 1
•Is this a function?
•Hint: Look only at the x-coordinates
NO
•Is this still a relation?
YES
10. Unit 4 - Relations and Functions
10
Choice One Choice Two
Example 5
3
1
0
–1
2
3
2
–1
3
2
3
–2
0
Which relation mapping represents a
function?
Choice 1
11. Unit 4 - Relations and Functions 11
Example 6
Which relation mapping represents a function?
A. B.
B
12. Unit 4 - Relations and Functions 12
Vertical Line Test
•Vertical Line Test: a relation is a function if a
vertical line drawn through its graph, passes
through only one point.
AKA: “The Pencil Test”
Take a pencil and move it from left to right (–
x to x); if it crosses more than one point, it is
not a function
13. Unit 4 - Relations and Functions 13
Vertical Line Test
Would this
graph be a
function?
YES
14. Unit 4 - Relations and Functions 14
Vertical Line Test
Would this
graph be a
function?
NO
15. Unit 4 - Relations and Functions 15
Is the following function discrete or continuous?
What is the Domain? What is the Range?
Discrete
-7, 1, 5, 7, 8, 10
1, 0, -7, 5, 2, 8
16. Unit 4 - Relations and Functions 16
Is the following function discrete or continuous?
What is the Domain? What is the Range?
continuous
8,8
6,6
17. Unit 4 - Relations and Functions 17
Is the following function discrete or continuous?
What is the Domain? What is the Range?
continuous
0,45
10,70
18. Unit 4 - Relations and Functions 18
Is the following function discrete or continuous?
What is the Domain? What is the Range?
discrete
-7, -5, -3, -1, 1, 3, 5, 7
2, 3, 4, 5, 7
19. Unit 4 - Relations and Functions 19
Example 7
Which situation represents a function?
There is only one price for each
different item on a certain date. The
relation from items to price makes it a
function.
A fruit, such as an apple, from the
domain would be associated with
more than one color, such as red and
green. The relation from types of fruits
to their colors is not a function.
a. The items in a store to their prices on a
certain date
b. Types of fruits to their colors
20. 20
Domain and Range in Real Life
The number of shoes in x pairs of shoes can be
expressed by the equation y = 2x.
What is the independent variable?
The # of pairs of shoes.
What is the dependent variable?
The total # of shoes.
Unit 4 - Relations and Functions
21. Unit 4 - Relations and Functions 21
Domain and Range in Real Life
Mr. Landry is driving to his hometown. It takes four hours to get
there. The distance he travels at any time, t, is represented by
the function d = 55t (his average speed is 55mph.
What is the independent variable?
What is the dependent variable?
The time that he drives.
The total distance traveled.
22. Unit 4 - Relations and Functions 22
Domain and Range in Real Life
Johnny bought at most 10 tickets to a concert for him and his
friends. The cost of each ticket was $12.50.
Complete the table below to list the possible domain and
range.
1 2 3
12.50 25.00 37.50
4
50
5
62.50
6 7 8 9 10
75 125
112.50
100
87.50
The number of tickets bought.
What is the dependent variable?
The total cost of the tickets.
What is the independent variable?
23. Unit 4 - Relations and Functions 23
Domain and Range in Real Life
Pete’s Pizza Parlor charges $5 for a large pizza with no
toppings. They charge an additional $1.50 for each of their 5
specialty toppings (tax is included in the price).
What is the independent variable?
The number of toppings
What is the dependent variable?
The cost of the pizza
