A function is a set of ordered pairs where each x-value is paired with exactly one y-value. The domain is the set of all possible x-values, and the range is the resulting y-values. To find the rate of change, use the difference quotient which is similar to the slope formula. The vertical line test determines if a graph represents a function - if any vertical line intersects the graph more than once, it is not a function. Domain restrictions specify allowed input values.
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.
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.
Discuss and apply comprehensively the concepts, properties and theorems of functions, limits, continuity and the derivatives in determining the derivatives of algebraic 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.
A Strategic Approach: GenAI in EducationPeter 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.
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.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
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.
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!
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
2. Let’s see how much you
remember
What is a function?
How do you find rate of change of a function?
How do you graph a function?
How can you know by looking at the graph something is a
function?
How do you find domain and range of a function?
3. Functions
A function is a set of ordered pairs of numbers (x,y) in
which no two distinct ordered pairs have the same first
number.
Write the definition of a function in your own words
The domain of a function is the set of all possible x values
or the input.
The range is the resulting values y, or the output, from the
given input values.
How do you know whether x or y is independent or
dependent?
4. Rate of change
The rate of change of a function is found by dividing the outputs by the inputs. Two
points are needed to calculate the rate of change.
Later on another way to calculate the rate of change is to use the difference quotient.
The difference quotient is
Or
How is the difference quotient similar to the slope formula?
f x + h( )- f (x)
h
f b( ) - f (a)
b - a
5. Graphs of Functions
If f is a function, then the graph of f is the set of all points
(x,y) in the plane R2 for which (x,y) is an ordered pair in f.
The Vertical Line Test determines whether a graph
represents a function.
Explain why the VLT test can show whether a graph is a
function.
7. Domain Restrictions
Domain restrictions are when the input values of a
function are restricted to certain values. Determine the
domain restrictions for the following functions and explain
your reasoning.
x
1
x
log x( )
8. General functions
Work with a partner to find the domain and range of the
following functions and graphs:
a) f(x)=x g) f(x)=1/x
b) f(x)=x2 h) f(x)=log(x)
c) f(x)=x3 i) f(x)=ex
d) f(x)= j) f(x)=sin(x)
e) f(x)={ 1-x if x<=1 k) f(x)=cos(x)
x2 if x>1
x
9. Types of functions
A function f is an even function if for every x in the domain
of f, f(-x)=f(x)
A function f is an odd function if for every x in the domain
of f, f(-x)=-f(x)
Given two functions f and g, the composite function,
denoted by (f°g)(x)=f(g(x))
and domain of f°g is the set of all numbers x in the domain of
g such that g(x) is in the domain of f.
10. Exercises
Prove whether the following functions are even, odd, or
neither.
1) f(x)=10x3-4x2+3x+8
2) f(x)=-7x7-x3+5x
3) f(x)=x3-x2-1
4) f(x)=2x2-3
12. Table of signs
The table of signs is created by looking at the signs of
parts of the function to see the overall change of the sign
of the function.
We look at the intervals of graph that are positive and
negative.
We can find the maximum and minimum values when we
look at the table of signs.
A minimum is when the sign of the graph changes
negative to a positive.
A maximum is when the signs changes positive to
negative.
13. For the function x3+4x2+x-6,
the table of signs is
Functio
n
-3 -2 1
x-1
- - - +
x+2
- - + +
x+3
- + + +
f(x)
- +
- +
Does the function have a max and/or a min? Give your reasoning.
14. Horizontal and Vertical asymptotes
To find the horizontal asymptote of rational functions in the
form
f(x)=(axn+…)/(bxm+…)
If n<m, then y=0 is the horizontal asymptote
If n=m the the horizontal asymptote is y=a/b
If n>m, then there no horizontal asymptote but an oblique
asymptote.
The vertical asymptote is found by setting the denominator
equal to zero.
15. Find the horizontal and vertical
asymptote
1) f(x)=(x2+3x+1)/(4x2-9)
2) f(x)=(x2-x-2)/(x-2)
3) f(x)=6x2-3x+4
4) f(x)=(x-12)/(2x3+5x-3)
16. Review
What is a function? Give an example of a function and a
non-function.
When does a function have a rate of change of zero?
When is the slope undefined?
What is the domain and the range of the function
f(x)=
The function y=x+1 changes from negative to positive at
the point x=-1. What does that indicate?
x^2-1