Unit 2 focuses on functions and their translations, reflections, and symmetries. Translations move the graph left/right or up/down, reflections flip or mirror the graph, and symmetries involve patterns that repeat on both sides of an axis. The document provides examples of translating and reflecting common parent functions like exponential and logarithmic functions. It also discusses symmetry in functions with respect to the y-axis (even functions), x-axis (odd functions), and origin. Homework problems are assigned from the textbook involving graphing functions and describing end behavior using limits.
Gives idea about function, one to one function, inverse function, which functions are invertible, how to invert a function and application of inverse functions.
Continuity, Removable Discontinuity, Essential Discontinuity. These slides accompany my lectures in differential calculus with BSIE and GenENG students of LPU Batangas
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
Gives idea about function, one to one function, inverse function, which functions are invertible, how to invert a function and application of inverse functions.
Continuity, Removable Discontinuity, Essential Discontinuity. These slides accompany my lectures in differential calculus with BSIE and GenENG students of LPU Batangas
Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics
¿Sin tiempo para el gimnasio?. Se acabaron tus excusas: !Muévete!Dr. Lázaro Poey
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The inverse of a function "undoes" the effect of the function. We look at the implications of that property in the derivative, as well as logarithmic functions, which are inverses of exponential functions.
The inverse of a function "undoes" the effect of the function. We look at the implications of that property in the derivative, as well as logarithmic functions, which are inverses of exponential functions.
Properties of Functions
Odd and Even Functions
Periodic Functions
Monotonic Functions
Bounded Functions
Maxima and Minima of Functions
Inverse Function
Sequence and Series
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
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.
Welcome to TechSoup New Member Orientation and Q&A (May 2024).pdfTechSoup
In this webinar you will learn how your organization can access TechSoup's wide variety of product discount and donation programs. From hardware to software, we'll give you a tour of the tools available to help your nonprofit with productivity, collaboration, financial management, donor tracking, security, and more.
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 French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
For more information, visit-www.vavaclasses.com
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
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.
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
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.
2. What do we need to do orWhat do we need to do or
change for Unit 2?change for Unit 2?
Things to keep:Things to keep: Things to change:Things to change:
3. TranslationsTranslations
First, you have to know what the parentFirst, you have to know what the parent
functions look like!functions look like!
Parent functions…Parent functions…
4.
5.
6. We did this in Alg 2!We did this in Alg 2!
Graph the parent function and move it!Graph the parent function and move it!
Ex:Ex:
Left or right?Left or right?
Up or down?Up or down?
Flip or normal?Flip or normal?
2
( 4) 5y x= − − +
7. New to Pre-Calc…New to Pre-Calc…
-f(x)-f(x)
If there is a negative in the front it is aIf there is a negative in the front it is a
reflection over the x-axis. (flip)reflection over the x-axis. (flip)
f(-x)f(-x)
If there is a negative on theIf there is a negative on the “inside” it is a“inside” it is a
reflection over the y-axis. (mirror imaged)reflection over the y-axis. (mirror imaged)
11. Symmetry - ExamplesSymmetry - Examples
w/ respect to the y-axisw/ respect to the y-axis (EVEN)(EVEN)
f(x) = xf(x) = x22
w/ respect to the x-axisw/ respect to the x-axis (ODD)(ODD)
x = yx = y22
w/ respect to the originw/ respect to the origin
f(x) = xf(x) = x33
