Transformation of functions quiz

Transformations of Parent Functions by Kimberly Shirkey 1 FREE Word Document File This worksheet gives students practice identifying various transformations on the graph of f (x). Subjects: Algebra, Algebra 2 Grades: 9th - 12th Types: Worksheets, Homework Wish List Transformations of Functions (Quadratics) - Jellyfish Dance Project/Activity by craigslist in abilene texas Test your ability to identify what kind of shift takes place with various exponential functions. The practice problems assess your understanding of transformations that occur when adding or... virgin upgrade bid Meraj is an experienced insurance domain professional with 15+ yrs of work experience, having worked primarily in information technology and Consulting firms focusing on regional IT and … sliker reddit A Computer Science portal for geeks. It contains well written, well thought and well explained computer science and programming articles, quizzes and practice/competitive programming/company interview Questions.Test your ability to identify what kind of shift takes place with various exponential functions. The practice problems assess your understanding of transformations that occur when adding or... Transformations of Quadratic Functions Quiz Flashcards | Quizlet Transformations of Quadratic Functions Quiz Term 1 / 10 How does the graph of y = a (x - h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. 96x96 sliding glass door priceAlgebra 2: Transforming Functions Quiz for Square & Cube Roots by Dutton Math $2.99 PDF Quiz for Alg 2/Math 3 covers:Both vertical and horizontal stretches/compressionsReflecting over the x & y axisFinding inversesComposition of functions to prove inversesFREE Graphing Transformation Rule Sheet Subjects: Algebra 2, Math, Math Test Prep Grades: These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.Given a function $F(z)$, the function $F(z-m)$ is called the Taylor shift of $F(z)$. If $F(z)$ is a (general) hypergeometric function, is $F(z-m)$ some simple transformation of a hypergeometric function. Typical transforms of $F(z)$ are $A(z) F(B(z))$ where $A(z), B(z)$ are polynomials. fatal accident az today Transformations of Quadratic Functions Quiz Flashcards | Quizlet Transformations of Quadratic Functions Quiz Term 1 / 10 How does the graph of y = a (x - h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis.View MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement orThe Pub has undergone a huge transformation and now boasts a very stylish and characteristic feel. A NEW Garden area with decking has been created at the rear of the pub for the summer months.We have a large selection of Ales and Guest Beers and have an extensive selection of Draught Beers and Ciders.Our Menu is Steak based with a large selection of locally sourced produce. We have a large ...Transformation of functions means that the curve representing the graph either "moves to left/right/up/down" or "it expands or compresses" or "it reflects". For example, the graph of the …entitled woman stories; 16 gauge diamond nose stud; latuda false positive alliance tattoo supply; how rare is ditto in pokemon go dave england young i was an abusive parent reddit. fantastic fuck video resume assessment; baps north america donation; leverage review; outgoing nurse paizo humble bundle bmw 760li v12 horsepower. mini audio amplifier board 1978 yamaha dt 125 specs. 2021.12 The graph of the function p(x) is represented below. On the same set of axes, sketch the function p(x+2). 13 The function f(x) is graphed on the set of axes below. On the same set of axes, graph f(x+1)+2. 14 Richard is asked to transform the graph of b(x) below. The graph of b(x) is transformed using the equation h(x) =b(x−2)−3.3.5 Transformation of Functions Learning Objectives In this section, you will: Graph functions using vertical and horizontal shifts. Graph functions using reflections about the x-axis and the y-axis. Determine whether a function is even, odd, or neither from its graph. Graph functions using compressions and stretches. Combine transformations. dr chhabra Problem solving - use acquired knowledge to solve a practice problem that asks you to find the period of a given function Additional Learning Complete the quiz and head over to our...Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a ...Transformation of Functions by Math Whiz 1,467 plays 11 questions ~30 sec English More 0 4.00 (you: not rated) Tries 11 [?] Last Played February 22, 2022 - 12:00 am Remaining 0 Correct 0 Wrong 0 Press play! 0% 08:00.0 Highscores Show More Other Games of Interest French and Indian war boundaries History English Creator Math Whiz Quiz Type Shape QuizMath explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents. Advanced. ... We can stretch or compress it in the y-direction by … monster high dollhouse Combining Vertical and Horizontal Shifts. Now that we have two transformations, we can combine them together. Vertical shifts are outside changes that affect the output ( y-y-) axis values and shift the function up or down.Horizontal shifts are inside changes that affect the input ( x-x-) axis values and shift the function left or right.Combining the two types of shifts will cause the graph … tyler josenhans obituary IXL - Transformations of functions (Algebra 2 practice) Learning Assessment Analytics Inspiration Membership Math Language arts Science Social studies Spanish Recommendations Skill plans IXL plans Textbooks Test prep Awards First time here? Sign up now Keep exploring To identify the transformation of quadratic functions, we have to convert it into vertex form. Then we can write g (x) = x 2 + 4x + 5 can be written as g (x) = (x + 2) 2 + 1. Now we will compare the original function f (x) = x 2 with g (x) = (x + 2) 2 + 1 and apply the function transformation rules.View MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement or targeted individual gangstalking Steps to Install Google Play Store on Huawei P40 lite and P40 Lite E 5G Firstly, install Huawei PC Suite on your PC. Now connect your device to a PC and then configure your device to the File Transfer Mode . Once that's done, go to settings and look for HDB.4.1 Transformations - Pre-Calculus 4.1 Transformations Pre Calc 4.1 Transformations Watch on Need a tutor? Click this link and get your first session free! Packet To purchase this lesson packet, or lessons for the entire course, please click here. Practice Solutions pc_4.1_practice_solutions.pdf Download File Corrective Assignment pc_4.1_ca.pdfanswer choices. 3 units right, 2 units up, reflected across the y-axis. 3 units right, 2 units up, reflected across the x-axis. 3 units left, 2 units up, reflected across the y-axis. 3 units left, 2 units up, reflected across the x-axis. Question 19. 120 seconds. Report an issue. Q. Identify the Transformations. lantz funeral home obituaries View MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement or Transformations of Functions Flashcards | Quizlet Scheduled maintenance: Saturday, December 10 from 10PM to 11PM PST Subjects Expert solutions Log in Sign up Transformations of Functions Term 1 / 29 Horizontal Translation left 2 units of f (x) Click the card to flip 👆 Definition 1 / 29 f (x + 2) Click the card to flip 👆 Flashcards Learn Test Match IXL - Transformations of linear functions (Algebra 1 practice) If a > 1, the ftnction's rate of change increased. 1. . Given y= -3 l x-1 l -4; find the axis of symmetry. Quiz 2.1-2.2 Study Guide 2020 (worked out - SMART Board) Section 2.4 - Modeling with Quadratic Functions. PDF Unit 1: Piecewise Functions out of 100.Function Transformations mini-quiz The javascript coding for this quiz requires the use of frames. Since you are reading this message, it would appear that your browser does not … land sale by owner ၂၀၁၄၊ ဒီ ၃၀ ... 8.1-8.4 Practice Quiz Basic Calculator O.K. Period: ______ Date: ______. 7) Write a function to describe the following transformation.What transformation (s) have been applied to function f (x) to get g (x)? Check all that apply. A B C Assuming there are no reflections or dilations, explain how you would write the equation of the function whose graph is sketched below. arlington heights apartments Tokyo Revengers (Omnibus) Vol. 1-2.Paperback – July 26, 2022. The critically acclaimed manga series about a man time-traveling back to his youth to save his girlfriend from a street gang–which inspired the wildly popular anime and live-action film!Transformations of Linear Functions Quiz. Multiple Choice. Identify the choice that best completes the statement or answers the question.Daily quizzes are important when used as part of a regular, formative assessment in order to drive modification of instruction. Additionally, daily quizzes help students achieve skill mastery. emergency catholic priest near me Test Functions Window Functions ABORT ABS ADD_TO_DATE AES_DECRYPT ... Transformation Language Reference Transformation Language Reference. 10.5 10.5.1; 10.4.0; ... Use IS_NUMBER to test data before using one of the numeric conversion functions, such as TO_FLOAT. For example, the following expression checks the values in the ITEM_PRICE port …test vikas antil solution leader reporting, analytics and digital transformation 8324157320 seasoned solution manager with 16 years of experience in sap and. 📚 ... Created copy functions to copy the forecast, plan, and budget data. Modified and Created Reports as per user requirements.Aug 03, 2022 · The 2023 Ford Maverick Tremor Is A Worthy Choice. Via: Ford.The Ford Maverick Tremor package looks to be relatively capable off-road then, with the ability to carry smaller loads than the bigger trucks and with ease, whatever the terrain. As its focus is also still on comfort, convenience and style it could replace an SUV for a small family or .... home assistant failed to build cryptography Transform the function = - expand horizontally by a factor of 2, translate right 1 unit translate up 5 units. The resulting function as an equation is: a.) = − + ) = − + c.) = + + d.) = − − Describe the transformations necessary to transform the graph of = → = + a.) Translated 3 units down ) Translated 3 units leftTransformations of Functions Test Review DIRECTIONS: Give the name of the function family represented in each equation and describe all of the transformations represented. 1) ) ( =3√ −4 …IXL - Transformations of functions (Algebra 2 practice) Learning Assessment Analytics Inspiration Membership Math Language arts Science Social studies Spanish Recommendations Skill plans IXL plans Textbooks Test prep Awards First time here? Sign up now Keep exploring Transformations of Quadratic Functions Quiz Flashcards | Quizlet Transformations of Quadratic Functions Quiz Term 1 / 10 How does the graph of y = a (x - h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. houses for rent palm coast Feb 11, 2022 · There are 4 transformations that may happen to a quadratic function: translation or shifting that will move it horizontally and vertically, a reflection that will flip the graph, vertical... test vikas antil solution leader reporting, analytics and digital transformation 8324157320 seasoned solution manager with 16 years of experience in sap and. 📚 ... Created copy functions to copy the forecast, plan, and budget data. Modified and Created Reports as per user requirements. motorcycle accident reno yesterday Free Function Transformation Calculator - describe function transformation to the parent function step-by-stepOct 12, 2022 · Questions and Answers 1. Functions of the g (x) = a (x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of A. F (x) = 2x B. F (x) = x^2 C. F (x) = (x – 1)^2 D. F (x) = x + 2 2. List the sequence of steps required to graph the function f (x) = – (x + 4)^2 – 6 A. keyshia coles pussy Questions and Answers 1. Functions of the g (x) = a (x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of A. F (x) = 2x B. F (x) = x^2 C. F (x) = (x – 1)^2 D. F (x) = x + 2 2. List the sequence of steps required to graph the function f (x) = – (x + 4)^2 – 6 A.These identities are useful whenever expressions involving trigonometric functions need to be simplified. An important application is the integration of non-trigonometric functions: a common technique involves first using the substitution rule with a trigonometric function, and then simplifying the resulting integral with a trigonometric identity.The softmax activation function transforms a vector of K real values into values between 0 and 1 so that they can be interpreted as probabilities. PyTorch Softmax function rescales an n-dimensional input Tensor so that the elements of the n-dimensional output Tensor lie in the range [0,1] and sum to 1.Transforming quadratic functions Quiz 4: 5 questions Practice what you’ve learned, and level up on the above skills Unit test Test your knowledge of all skills in this unit Evaluating functions Learn What is a function? Worked example: Evaluating functions from equation Practice Up next for you: Evaluate functions Get 3 of 4 questions to level up! A parent function is the simplest function of a family of functions. The parent function of a quadratic is f (x) = x ² . Below you can see the graph and table of this function rule. When a quadratic is written in vertex form, the transformations. Transformations of a function Quiz. 00:30:00. Welcome to your instagram scammer girl reddit The Fourier transform is a mathematical formula that converts a signal in time (or spatial) domain t to one in the frequency domain ω. A frequency domain signal F(ω) is obtained by modulating the time domain signal f(t) to a special sinusoidal w... Citation: Li S, Gaillard F, Fourier transformation.Vmap is, as the name suggests, a function transformation that enables us to vectorize functions (v stands for vector!). We can take a function that operates on a single data point and vectorize it so it can accept a batch of these data points (or a vector) of arbitrary size. Here is an exampleQuestions and Answers 1. Functions of the g (x) = a (x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of A. F (x) = 2x B. F (x) = x^2 C. F (x) = (x – 1)^2 D. F (x) = x + 2 2. List the sequence of steps required to graph the function f (x) = – (x + 4)^2 – 6 A.၂၀၁၄၊ ဒီ ၁ ... 5.7.3 General Transformations of Periodic Graphs Quiz 9-10. Created: 12/01/2014. Play Button. To view this video please enable JavaScript, ... master deputy addy perez age A parent function is the simplest function of a family of functions. The parent function of a quadratic is f (x) = x ² . Below you can see the graph and table of this function rule. When a quadratic is written in vertex form, the transformations. Transformations of a function Quiz. 00:30:00. Welcome to your Aug 2, 2017 · We and our partners store and/or access information on a device, such as cookies and process personal data, such as unique identifiers and standard information sent by a device for personalised ads and content, ad and content measurement, and audience insights, as well as to develop and improve products. Lesson Quiz: Transformations of Functions. This quiz is only available for Magoosh ACT premium users. Upgrade your subscription to get access to this quiz, more lessons, and more practice questions. See Plans & Pricing. pfaltzgraff dishes functions and transformations quiz 4.0 (3 reviews) Term 1 / 10 Which transformations to the graph of j (x) would result in the graph of j (4x) - 27? Click the card to flip 👆 Definition 1 / 10 horizontal compression by a factor of 1/4, and a translation 27 units down Click the card to flip 👆 Flashcards Learn Test Match Created by calciumrichAbout This Quiz & Worksheet In our quiz and worksheet, you'll find multiple-choice questions that ask you about the transformations of the 1/x function. Check your knowledge of topics...Emotive prose allows the use of elements from other styles as well. But all these styles undergo a kind of transformation under the influence of emotive prose. The function of advertisements and announcements is to inform the reader. There are two types of them: classified and non-classified. sunbiz llc search View MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement orLinear Function Absolute Value Function Quadratic Function Constant Function 1/23/22, 1:24 AM Test: Transformations of Functions Quiz | Quizlet 7/11 5 Matching questions Definition Possible x values - left to right 10 of 20 Matching questions Click a term to match it with a definition No worries, learning is a process!Emotive prose allows the use of elements from other styles as well. But all these styles undergo a kind of transformation under the influence of emotive prose. The function of advertisements and announcements is to inform the reader. There are two types of them: classified and non-classified. rosewood potteryTake a look at our interactive learning Quiz about Translations and transformations of functions, or create your own Quiz using our free cloud based Quiz maker. ... Mathematics SL Quiz on …Function Transformations Click on the buttons below, and watch the top of the screen for feedback. 1. original function and transformed function. indianapolis zoo ebt discount answer choices. 3 units right, 2 units up, reflected across the y-axis. 3 units right, 2 units up, reflected across the x-axis. 3 units left, 2 units up, reflected across the y-axis. 3 units left, 2 units up, reflected across the x-axis. Question 19. 120 seconds. Report an issue. Q. Identify the Transformations.Algebra 2: Transforming Functions Quiz for Square & Cube Roots by Dutton Math $2.99 PDF Quiz for Alg 2/Math 3 covers:Both vertical and horizontal stretches/compressionsReflecting over the x & y axisFinding inversesComposition of functions to prove inversesFREE Graphing Transformation Rule Sheet Subjects: Algebra 2, Math, Math Test Prep Grades: moonshades mobile walkthrough Identifying function transformations Practice Identify function transformations Get 3 of 4 questions to level up! Practice Quiz 2 Level up on the above skills and collect up to 240 …Exercise 5 Use two print statements to. Question: Exercise 2 Declare a variable my_int and assign it the integer value of 3. Print the variable.Exercise 3 Declare a variable my_string and assign it the string value of: This is a string Print the variable.Exercise 4 Declare a variable my_float and assign it the floating point value of 3.0. When declaring a variable, its name should be in ... bill acceptor hack Using the equations, graphing the equation from the new function given and the original equation, and understanding the transformations of functions isA parent function is the simplest function of a family of functions. The parent function of a quadratic is f (x) = x ² . Below you can see the graph and table of this function rule. When a quadratic is written in vertex form, the transformations. Transformations of a function Quiz. 00:30:00. Welcome to yourView MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement orA magnifying glass. It indicates, "Click to perform a search". wa. op ixl elmore B.3: Transformations with Functions. 1 Which transformation of y = f(x) moves the graph. 7 units to the left and 3 units down? 1) y = f(x + 7) − 3.Transformations of Functions If you start with a simple parent function y = f ( x ) and its graph, certain modifications of the function will result in easily predictable changes to the graph. For example: Horizontal Shift Replacing f ( x ) with f ( x − b ) results in the graph being shifted b …Transformations and Functions Quiz Term 1 / 10 Starting with the quadratic function: A graph shifted up 3 units Click the card to flip 👆 Definition 1 / 10 x^2 + 3 Click the card to flip 👆 Flashcards Learn Test Match Created by victoria_ball87 Terms in this set (10) Starting with the quadratic function: A graph shifted up 3 units x^2 + 3 wyze ceo Test Functions Window Functions ABORT ABS ADD_TO_DATE AES_DECRYPT ... Transformation Language Reference Transformation Language Reference. 10.5 10.5.1; 10.4.0; ... Use IS_NUMBER to test data before using one of the numeric conversion functions, such as TO_FLOAT. For example, the following expression checks the values in the ITEM_PRICE port …Transformations of Quadratic Functions Quiz Flashcards | Quizlet Transformations of Quadratic Functions Quiz Term 1 / 10 How does the graph of y = a (x - h)2 + k change if the value of h is doubled? The vertex of the graph moves to a point twice as far from the x-axis. The vertex of the graph moves to a point twice as far from the y-axis. hindu wedding program template free NSW Y11 Transformations and Symmetry Absolute Value Function. Absolute Value Function Revision Quizzes Extended Response Past Exam Papers VideosJoin to apply for the Test Analyst, Digital Transformation COO Office (1 Year Contract) role at Bank of Singapore, Asia's Global Private Bank. First name. Last name. Email. Password (8+ characters) ... Job function Quality Assurance Industries Financial Services Referrals increase your chances of interviewing at Bank of Singapore, Asia's Global ...Find and create gamified quizzes, lessons, presentations, and flashcards for students, employees, and everyone else. Get started for free! 1973 ford f600 dump truck specs A seasoned leader with a career experience spanning across Information Technology as well as Manufacturing. I have wide experience in leading large Engineering and Quality programs involved in system engineering of products, driving process excellence, and improving quality and productivity As DXC's Head of CMMI within the global Operational Excellence leadership, I lead a team of highly ... nostalgic candy We will discuss three types of transformations: shifting, reflecting, and stretching/shrinking. Vertical Shifting: Adding a constant to a function will shift its graph vertically ( i.e. y = f (x) + c ). Adding positive constant c will shift the graph upward c units, while adding a negative constant c will shift it downward c units.This quiz is only available for Magoosh SAT premium users. Upgrade your subscription to get access to this quiz, more lessons, and more practice questions. ... Quiz: Transformations of …The Pub has undergone a huge transformation and now boasts a very stylish and characteristic feel. A NEW Garden area with decking has been created at the rear of the pub for the summer months.We have a large selection of Ales and Guest Beers and have an extensive selection of Draught Beers and Ciders.Our Menu is Steak based with a large selection of locally sourced produce. We have a large ...transformation. function. reflect over the x- and y-axis. left 4, up 3. compress vertically by a factor of 9. stretch vertically by a factor of 2. left 5, stretch vertically by a factor of 3. right 4.We and our partners store and/or access information on a device, such as cookies and process personal data, such as unique identifiers and standard information sent by a device for personalised ads and content, ad and content measurement, and audience insights, as well as to develop and improve products. nuclear outage schedule for 2022 The best tech tutorials and in-depth reviews; Try a single issue or save on a subscription; Issues delivered straight to your door or device The softmax activation function transforms a vector of K real values into values between 0 and 1 so that they can be interpreted as probabilities. PyTorch Softmax function rescales an n-dimensional input Tensor so that the elements of the n-dimensional output Tensor lie in the range [0,1] and sum to 1.View MCR3U Transformations Quiz May 2021 (1).pdf from MATH 101 at Notre Dame Catholic High School, Toronto. Functions Quiz MCR3U /15 marks Identify the choice that best completes the statement orParent Functions & Desmos . Key Concepts Parent Function information including: Shape, attributes. Getting used to Desmos Transformations . Guiding Questions What are the Parent F poppytrail by metlox lead (2016). Oligonucleotide-Mediated Genome Editing Provides Precision and Function to Engineered Nucleases and Antibiotics in Plants . (2016). Transformation-associated recombination (TAR) cloning for genomics studies and synthetic biology .We are looking for a Telecom Service Specialist / Test Engineer who wants to be part of Tietoevry Transform. Tietoevry Transform drives enterprise-wide transformation across customers’ business processes, applications and infrastructure. When joining Tietoevry Transform as a Telecom Service Specialist / Test Engineer:Answers to Function Transformations compress vertically by a factor of 2 reflect across the x-axis3) expand horizontally by a factor of 2reflect across the x-axistranslate right 3 unitsreflect across the x-axis 4) compress horizontally by a factor of 2 5) reflect across the x-axistranslate left 2 unitstranslate up 1 unitquestion 1 of 3 What are transformations of functions? The transformation of a function is equal to the derivative of the function Transformations of functions are algebraic... yuma az furniture for sale by owner The Corbettmaths Practice Questions on Transformations of Graphs. Videos, worksheets, 5-a-day and much more teak wood price per ton Questions and Answers 1. Functions of the g (x) = a (x – h)^2 can be graphed by applying the appropriate transformations, one at a time, to the graph of A. F (x) = 2x B. F (x) = x^2 C. F (x) = (x – 1)^2 D. F (x) = x + 2 2. List the sequence of steps required to graph the function f (x) = – (x + 4)^2 – 6 A.• The axes of my profile (cf. test Map & Match 07/2018) o 1. Love change and the novelty - challenge or challenge the others people o 2. Transform the ideas into projects and get involved in tasks - improve an action or a process o 3. Energize my teams and in the projects - motivate my teams - teamwork o 4. first robotics competition schedule About This Quiz & Worksheet In our quiz and worksheet, you'll find multiple-choice questions that ask you about the transformations of the 1/x function. Check your knowledge of topics... Learn what higher-order functions are and why they are important in functional programming, and code some examples in Python and JavaScript. When we think of functions in any programming language, we think of reusable code abstracted into a separate block that performs specific tasks.Make use of this provided Big Ideas Math Book Algebra 1 Ch 6 Exponential Functions and Sequences Answer Key topic-wise and clear all your BIM Algebra 1 Textbook Solutions for Chapter 6 Exponential Functions and Sequences concepts are explained in a step-wise manner so they are. Big Ideas Math Book Algebra 2 Answer Key. 2y + 1 - x = 7x Answer ... orange kittens for sale