Apply the concepts you've learned to make you test-ready. You can identify a y-transformation as changes are made outside the brackets of y=f(x). 4. f(x) 5 x2 1 4 5. f(x) 5 (x 1 3)2 6. f(x) 5 x2 2 2 7. f(x) 5 (x 2 5)2 8. f(x) 5 x2 1 6 9. f(x) 5 (x 1 1)2 What are the This quiz is incomplete! f (x) upward . Possible equation matches (not in matching order): Edit. The table of values for f(x) and g(x) are as shown below. The graph of y = f(x) 3 is modi ed outside the f (so it is a vertical change) and since it is f(x) 3 this is shifted down 3. Horizontal Translation 2. Consider the relationship between Fahrenheit and Celsius temperatures.Â Using your graphing calculator, graph these two functions on the same set of axes: At what temperature are the Fahrenheit and Celsius readings the same? This fascinating concept allows us to graph many other types of functions, like square/cube root, exponential and logarithmic functions. Edit. Graph transformations of parent functions such as: square root, cube root, quadratic, cubic, absolute value, and greatest integer functions. a year ago. One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. c . The shape of a roof is modeled by a transformation of the absolute value function, f ( x) = | x |. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function.In other words, we add the same constant to the output value of the function regardless of the input. Delete Quiz. 1-5 Assignment - Parent Functions and Transformations. Create a table for the … Share practice link. U3D4_T Reflections of Functions. Exponential Functions Topics: 1. Practice Questions. Exercise this myriad collection of printable transformation worksheets to explore how a point or a two-dimensional figure changes when it is moved along a distance, turned around a point, or mirrored across a line. f xc + Shift . Improve your skills with free problems in 'Transformations of functions' and thousands of other practice lessons. Reflection through the x-axis 4. Identifying function transformations. 4. … When examining the formula of a function that is the result of multiple transformations, how can you tell a horizontal shift from a vertical shift? 6. The practice problems assess your understanding of transformations that occur when adding or subtracting numbers to the function or exponent. There are 12 problems with coordinate grid provided I you need more practice you can do more than 2 lessons. Collectively, these are known as the graphs of the . units . A function f( x ) f( x ) is given in Table 2. The line segments shown are straight and intersect at the point (4,-2). For example, if we are going to make transformation of a function using reflection through the x-axis, there is a pre-decided rule for that. 3) f (x) x g(x) x 4) f(x) x g(x) (x ) Transform the given function f(x) as described and write the resulting function as an equation. Reflection through the y-axis 5. Improve your math knowledge with free questions in "Transformations of functions" and thousands of other math skills. Sketch a graph of . Next lesson. A y-transformation affects the y coordinates of a curve. 1-5 Guided Notes SE - Parent Functions and Transformations. 9th - 11th grade . Transformations of Functions - Mystery Code ActivityStudents will practice identifying transformations of functions from their parent function given the transformed function. A function k (x) is defined as. Graphing exponential functions. Sketch the graph of each function below on the given graph. Played 0 times. Transformations of Functions DRAFT. What is a, the starting term, for the function: f(x) = 300(1.16) x ? Videos, worksheets, 5-a-day and much more 1-5 Exit Quiz - Parent Functions and Transformations. There are two other transformations, but they're harder to "see" with any degree of accuracy. To see what this looks like, compare the graphs of 2 × f (x) = 2x 2, f (x) = x 2, and ½ × f (x) = (½) x 2, below: 1-5 Guided Notes SE - Parent Functions and Transformations. This website and its content is subject to our Terms and Conditions. Downward shift: , this is a shift in y. Share practice link. Play. Graphing transformations of exponential functions. U3D3 Extra Practice 1 SOLUTIONS Function Notation & Translations . 4. Transformation of the graph of . Improve your math knowledge with free questions in "Transformations of functions" and thousands of other math skills. Learn. The different types of transformations which we can do in the functions are 1. Vertical Expansions and Compressions How different types of transformations occur in terms of x-coordinate and y-coordinate have been summarized below. vertical shift 5 units down . To log in and use all the features of Khan Academy, please enable JavaScript in your browser. Home Embed All High School Math Resources . practice sessions. Practice: Identify function transformations. Graphical Transformations of Functions In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. When you are ready to move on, call me over and I will assign you a Marbleslide Activity. 0. Which description does not accurately describe this functions transformation(s) of f(x) = ⅔(x - 7) 2 from the parent function? Practice the concept of function scaling and the relationship between its algebraic and graphical representations. In this section let c be a positive real number. 11/15/2018 1.6 Transformations of Functions - PRACTICE TEST WEEK 2 TEST - … Just like Transformations in Geometry, we can move and resize the graphs of functions: Let us start with a function, in this case it is f(x) = x 2, but it could be anything: f(x) = x 2. Transformations of functions: Horizontal translations. a.Â Determine an expression for h(x), if h(x) = f (-x). This is a transformation of the function f (t) = 2 t. shown in . Delete Quiz. U3D3 Extra Practice 2 Function Notation. Describe the transformations necessary to transform the graph of f(x) into that of g(x). Practice. Transformations of Functions Practice Problems DRAFT. Khan Academy Video: Shifts & Reflections of Root Function. To play this quiz, please finish editing it. c >0 : Function. Displaying top 8 worksheets found for - Transformations Of Functions Practice. Exponential growth and decay by a factor. Gravity. This quiz is incomplete! Horizontal Expansions and Compressions 6. Edit. Print; Share; Edit; Delete; Host a game. Edit. Library Functions: In previous sections, we learned the graphs of some basic functions. Transformations of Functions . is, and is not considered "fair use" for educators. Print; Share; Edit; Delete; Host a game. U3D3 Extra Practice 2 Solutions Function Notation : 4 3.4: U3D4_S Reflections of Functions. Choose: g(x) = x2 - 7. g(x) = x2 + 1. g(x) = x2 + 7. g(x) = x2 - 1. Function Transformations A reflectionis a movement where a graph “flips” over an axis (or another designated line of reflection). Khan Academy Video: Shifts & Reflections of Root Function. 0. Improve your math knowledge with free questions in "Transformations of functions" and thousands of other math skills. 2. Finish Editing. y-transformations. Transformations of Functions – Explanation & Examples. 1-5 Bell Work - Parent Functions and Transformations. Donate or volunteer today! The x coordinates are unaffected but all the y coordinates go up by 4. 4-1 Practice Form K Quadratic Functions and Transformations Graph each function. (3) y = (Â½ â¢ x)2 - 1, Topical Outline | Algebra 2 Outline| MathBitsNotebook.com | MathBits' Teacher Resources To play this quiz, please finish editing it. 1-5 Exit Quiz - Parent Functions and Transformations. 1-5 Assignment - Parent Functions and Transformations. by lorizych. U3D3 Extra Practice 2 Function Notation. (3) Graph the functions f(x) = x 3 and g(x) = 3 √x on the same coordinate plane. Solution (4) Write the steps to obtain the graph of the function y = 3(x − 1) 2 + 5 from the graph y = x 2 Solution U3D3 Extra Practice 2 Solutions Function Notation : 4 3.4: U3D4_S Reflections of Functions. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Solo Practice. U3D3 Extra Practice 1 SOLUTIONS Function Notation & Translations. 18. Sketch a graph of k (t). Parent Functions and Transformations Worksheet, Word Docs, & PowerPoints. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function.In other words, we add the same constant to the output value of the function regardless of the input. 5. Independent Practice 1. o. 0% average accuracy. Homework. Move 3 spaces down: w (x) = x3 − 4x − 3. All transformations are included: horizontal and vertical shifting (up, down, right, left) horizontal and vertical stretching and compressing; flip over x- and y-axis. View 1.6 Transformations of Functions - PRACTICE TEST.pdf from MATH 111 at American Military University. How is each graph a translation of f(x) 5 x2? Mathematics. Loading... Students will practice describing function transformations using words as well as algebraic notation. To help you visu… Tes Global Ltd is registered in England (Company No 02017289) with its registered office … (2) y = Â½ (x2 - 1) 21. Homework. ccamathteach. Solving exponential equations using exponent rules. Upward shift: , this is a shift in y. Transformations of Functions Practice. c.Â Rotate f (x) 90Âº about the origin. Explain how the graphs of y = f(x) = x3 and y = f(x) 3 are related. 1-5 Bell Work - Parent Functions and Transformations. Again, the “parent functions” assume that we have the simplest form of the function; in other words, the function either goes through the origin \left( {0,0} \right), or if it doesn’t go through the origin, it isn’t shifted in any way.When a function is shifted, stretched (or compressed), or flipped in any way from its “parent function“, it is said to be transformed, and is a transformation of a function.T-charts are extremely useful tools when dealing with transformations of functions. Write. Assume that the parent function was Transformations of functions: Vertical translations. Label the following as transformations on the independent variable or the dependent variable and describe the transformation. Vertical Translations A shift may be referred to as a translation. Play. Finding an exponential function given its graph. Practice Algebra Geometry Number Theory Calculus Probability Basic Mathematics Logic Classical Mechanics Electricity and Magnetism ... With function transformations, it's important to distinguish changes that happen before the main function is applied (essentially, changing the input) to those that happen after the main function is applied (changing the output). Terms of Use Contact Person: Donna Roberts, Describe the transformations that would produce the graph of the second function from the graph of the first function, for sections, Write the equation for the graph shown at the right. 2. Practice. This quiz is incomplete! Khan Academy is a 501(c)(3) nonprofit organization. Solo Practice. 3) f (x) x g(x) x 4) f(x) x g(x) (x ) Transform the given function f(x) as described and write the resulting function as an equation. Mathematics. Transformations of Functions An alternative way to graphing a function by plotting individual points is to perform transformationsto the graph of a function you already know. 5) f (x) x expand vertically by a factor of 11/15/2018 1.6 Transformations of Functions - PRACTICE TEST WEEK 2 TEST - … Function Transformations; 1.5 Section Exercises Verbal. We have already seen the different types of transformations in functions. This activity includes horizontal and vertical translations, reflections in the x-axis and y-axis, vertical dilations, and ho High School Math : Transformations of Polynomial Functions Study concepts, example questions & explanations for High School Math. Exponential decay: Half-life. The graph of f (x) is shown at the right on the domain [-3,3]. 5) f (x) x expand vertically by a factor of 1. y 5 4x2 2. f(x) 523x2 3. y 52 2 1 x2 Graph each function. b.Â Determine an expression for g(x), if g(x) is represented by the rotation of 180Âº of f (x) about the origin. If you're seeing this message, it means we're having trouble loading external resources on our website. 64% average accuracy. Identifying Vertical Shifts. 4. Move 4 spaces right: w (x) = (x−4)3 − 4 (x−4) Move 5 spaces left: w (x) = (x+5)3 − 4 (x+5) graph. Transformations of functions: Horizontal stretches. In other words, we add the same constant to the output value of the function regardless of the input. 8/19/2019 1.6 Transformations of Functions - PRACTICE TEST WEEK 2 TEST - SECTIONS 1.5 - Play this game to review Algebra II. Problem solving - utilize your skills to solve practice problems involving transformations Additional Learning. In Algebra 1, students reasoned about graphs of absolute value and quadratic functions by thinking of them as transformations of the parent functions |x| and x². Access this online resource for additional instruction and practice with transformation of functions. library functions. View 1.6 (2) Transformations of Functions - PRACTICE TEST.pdf from MATH 111 at American Military University. Vertical Translation 3. Solo Practice. PLAY. Save. Spell. f (x) f xc + Shift . Shifting a Tabular Function Vertically. Graphical Transformations of Functions In this section we will discuss how the graph of a function may be transformed either by shifting, stretching or compressing, or reflection. Transformations Of Linear Functions. Created by. Describe the transformations necessary to transform the graph of f(x) into that of g(x). The function is reflected in the x -axis, and translated 8 units up and 10 units to the right to create the roof model. STUDY. Date introduction to functions Transformations of Functions. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. Shifts. 7. Practice. Practice: Identify function transformations. RULES FOR TRANSFORMATIONS OF FUNCTIONS . Some of the worksheets for this concept are Transformations of graphs of linear functions, Translation, Linear, 1 exploration transformations of the absolute value function, Chapter 6 linear transformation, Linear functions work answers, Math 1330, 4 1 exponential functions and their graphs. What happens when f(x) = x 4 is translated 3 units to the left and 6 units downward? An alternative way to graphing a function by plotting individual points is to perform transformations to the graph of a function you already know. o. To play this quiz, please finish editing it. Transformations include combinations of vertical or horizontal stretches, translations, and reflections. Our mission is to provide a free, world-class education to anyone, anywhere. TRANSFORMATIONS OF FUNCTION WORKSHEET FOR 11TH GRADE (1) For the curve y = x 3 given in Figure, draw (i) y = −x 3 (ii) y = x 3 + 1 (iii) y = x 3 − 1 (iv) y = (x + 1) 3 with the same scale. a. Khan Academy: Identifying Transformations: p. 203 #1c, 2abc, 3, 5, 7, 10. Finish Editing. Flashcards. CREATE AN ACCOUNT Create Tests & Flashcards. One kind of transformation involves shifting the entire graph of a function up, down, right, or left. (1) y = 2 (x2 - 1) 11th - University grade . In this section let c be a positive real number. Test. In this unit, we extend this idea to include transformations of any function whatsoever. Summary of Transformation Graphs of square and cube root functions. Label the following as transformations on the independent variable or the dependent variable and describe the transformation. k (x) = f (x … c. units . View 1.6 Transformations of Functions - PRACTICE TEST.pdf from MATH 111 at American Military University. for which x = -1, under the rotation. horizontal shift to the right 2 units. This video is about Answer Key_Practice with Transformations of Functions For a function [Math Processing Error]g(x)=f(x)+k, the function [Math Processing Error]f(x) is shifted vertically [Math Processing Error]kunits. U3D4_T Reflections of Functions. Identifying Vertical Shifts. answer choices . (These are not listed in any recommended order; they are just listed for review.) The first of these transformation is multiplication on the entire function. This is the currently selected item. f (x) downward . If . Played 880 times. 11. Graph transformations of parent functions such as: square root, cube root, quadratic, cubic, absolute value, and greatest integer functions. b.Â On the same axes, graph the surface area of the cube as a function of x. c.Â Describe the relationship between these two graphs using transformational terms. Live Game Live. Enjoy the videos and music you love, upload original content, and share it all with friends, family, and the world on YouTube. Play. Write an equation for the transformed function. Find the coordinates of the point(s) Explain your results. Match. Precalculus: Graphical Transformations Practice Problems 3. Delete Quiz. The javascript coding for this quiz requires the use of frames. Live Game Live. Displaying top 8 worksheets found for - Transformations Of Linear Functions. Example: the function v (x) = x 3 − 4x. The graph of y = x3 is a cube function (blue). U3D4 Textbook … One simple kind of transformation involves shifting the entire graph of a function up, down, right, or left. Independent Practice 1. f xc − Shift . Here are some things we can do: Move 2 spaces up: w (x) = x3 − 4x + 2. Function Transformations. Fun maths practice! The practice problems assess your understanding of transformations that occur when adding or subtracting numbers to the function or exponent. Parent Functions and Transformations Worksheet, Word Docs, & PowerPoints. b. Graph the transformed function. The Corbettmaths Practice Questions on Transformations of Graphs. Save. Practice Transformations: Pick at least 2 lessons to complete. A common model for learning has an equation similar to where is the percentage of mastery that can be achieved after practice sessions. Reflection across the y-axis: y = f (− x) y = f(-x) y = f (− x) 19. Please read the ". Combine your knowledge of transforming functions to try out these practice problems. Stretch it by 2 in the y-direction: w (x) = 2 (x3 − 4x) = 2x3 − 8x. f x. is the original function, a > 0 and . This is a transformation of the function shown in . Function Transformations mini-quiz. Transformations Of Functions Practice - Displaying top 8 worksheets found for this concept.. Finish Editing. Example Questions . 17. Transformations include combinations of vertical or horizontal stretches, translations, and reflections. This equation combines three transformations into one equation. 3 years ago. Displaying top 8 worksheets found for - Transformations Of Linear Functions. ... Let’s go ahead and remove the parent function to show h(x) by itself. horizontal stretch by a factor of 3. horizontal compression by a factor of 1/4. vertical shift 6 units up. First, remember the rules for transformations of functions. 8 Diagnostic Tests 613 Practice Tests Question of the Day Flashcards Learn by Concept. There are 12 problems with coordinate grid provided. Reflection across the x-axis: y = − f (x) y = -f(x) y = − f (x) 20. The simplest shift is a vertical shift, moving the graph up or down, because this transformation involves adding a positive or negative constant to the function. Share practice link. The rule we apply to make transformation is depending upon the kind of transformation we make. Find f g and graph it on the plane as well. One kind of transformation involves shifting the entire graph of a function up, down, right, or left. The, Write the equation for the graph of function. from this site to the Internet Some of the worksheets for this concept are Transformations of graphs of linear functions, Translation, Linear, 1 exploration transformations of the absolute value function, Chapter 6 linear transformation, Linear functions work answers, Math 1330, 4 1 exponential functions and their graphs. b.Â At what temperature are the Fahrenheit and Celsius readings the same? Terms in this set (44) horizontal shift to the left 1 unit. This equation combines three transformations into one equation. y = | x |. by 600021357. Date introduction to functions Transformations of Functions. It is called a reflection because it will be a mirror image of the original. Loading... Students will practice describing function transformations using words as well as algebraic notation. Subjects: 1. Transformations necessary to transform the graph of f ( -x ) = 2x3 − 8x practice! G and graph it on the given graph to show h ( x ) f ( x x. Which x = -1, under the rotation for this quiz requires the of. Solutions function Notation & Translations the transformations necessary to transform the graph of y = (! Displaying top 8 worksheets found for - transformations of graphs combine your knowledge of transforming Functions to try these. After practice sessions log in and use all the features of khan:... Recommended order ; they are just listed for review. in y for which x -1... The domains *.kastatic.org and *.kasandbox.org are unblocked 523x2 3. y 52 1... 'Re having trouble Loading external resources on our website [ -3,3 ] you need more practice you can:! Similar to where is the original following as transformations on the plane as well at the right on plane. Concept allows us to graph many other types of transformations that occur when adding or subtracting numbers the... Considered `` fair use '' for educators are two other transformations, but they harder. Function to show h ( x ) into that of g ( x Solo. Individual points is to perform transformations to the function v ( x ) is given in 2. What is a transformation of the function v ( x ), if h ( x ) is as. Readings the same constant to the Internet is, and Reflections Functions and Worksheet... Use all the features of khan Academy, please finish editing it, if h ( x =! You 've learned to make transformation is depending upon the kind of transformation involves shifting the entire function of! On transformations of Functions, like square/cube Root, exponential and logarithmic Functions, under the rotation Corbettmaths questions... Graph each function below on the entire function than 2 lessons to complete, under the rotation utilize skills... X3 is a, the starting term, for the function regardless of the function of! Worksheet, Word Docs, & PowerPoints resources on our website do in the y-direction: w ( x is... Function k ( x ) by itself to move on, call over... ( transformations of functions practice ) horizontal shift to the left 1 unit c.â Rotate f ( x ) = 2x3 8x... Types of transformations that occur when adding or subtracting numbers to the output value the... Questions on transformations of graphs between its algebraic and graphical representations: transformations of Functions '' and thousands other! To make you test-ready make transformation is multiplication on the entire function compression by a factor practice... Or left problems involving transformations additional learning first of these transformation is multiplication on the [. A Marbleslide Activity Functions '' and thousands of other math skills graph a translation of f ( ). Many other types of transformations occur in terms of x-coordinate and y-coordinate have been summarized below when adding subtracting... Test.Pdf from math 111 at American Military University: Pick at least 2 lessons are made outside brackets!, 2abc, 3, 5, 7, 10 transformations of functions practice ’ s go ahead and the. Absolute value function, a > 0 and terms and Conditions affects the coordinates... We apply to make transformation is multiplication on the entire graph of a is... 523X2 3. y 52 2 1 x2 graph each function below on the independent variable or dependent...:, this is a transformation of the function v ( x ) are shown. What happens when f ( x … Solo practice these practice problems = | x | additional instruction practice..., please make sure that the Parent function was y = | x | shown.. Please finish editing it kind of transformation transformations of functions practice make call me over i... More than 2 lessons ready to move on, call me over and i will you... And describe the transformations necessary to transform the graph of a roof is modeled a... The right on the entire function in y function or exponent understanding of transformations which we can do in y-direction... The Parent function was y = x3 − 4x + 2 but all y! For learning has an equation similar to where is the original is the original, or left variable the... As a translation translation of f ( x ) is given in table 2 review Algebra II at. Not listed in any recommended order ; they are just listed for review. upon the kind of transformation make! Where is the original function, f ( x ) into that of g ( x 523x2! Function was y = f ( x ) = x3 and y = x!, anywhere Celsius readings the same constant to the left 1 unit using as. Use all the y coordinates go up by 4 on our website i you more! Explain how the graphs of the input of frames function to show h ( ). 3. y 52 2 1 x2 graph each function Flashcards Learn by.. Occur when adding or subtracting numbers to the function regardless of the absolute value function, a 0... Editing it u3d4 Textbook … Access this online resource for additional instruction and practice with transformation of practice! Their Parent function to show h ( x ) is given in table 2 Root function the x are... Multiplication on the given graph a positive real number positive real number on, call me over i... The rules for transformations of Functions to anyone, anywhere to graphing a function by plotting individual points is provide... Plotting individual points is to provide a free, world-class education to anyone,.! More than 2 lessons of these transformation is multiplication on the entire function for learning an... Much more transformations of Functions from their Parent function given the transformed function of Functions '' and of... Word Docs, & PowerPoints the origin multiplication on the given graph 3 − 4x and Functions. Parent Functions and transformations Worksheet, Word Docs, & PowerPoints spaces up: w ( x f. Provide a free, world-class education to anyone, anywhere: in previous sections, extend! Common model for learning has an equation similar to where is the.! Requires the use of frames x | # 1c, 2abc, 3, 5, 7 10! Domain [ -3,3 ] the function regardless of the function shown in make you test-ready 613 practice Tests of., down, right, or left and practice with transformation of the Video: Shifts Reflections. ( x ) and g ( x ) = x3 − 4x + 2 top... Upon the kind of transformation we make it by 2 in the Functions are.! Pick at least 2 lessons our website as well as algebraic Notation our is! A function by plotting individual points is to provide a free, world-class education to anyone,.. 1 unit behind a web filter, please finish editing it to make you.. 2 ( x3 − 4x: U3D4_S Reflections of Functions practice - displaying top 8 found... Scaling and the relationship between its algebraic and graphical representations an equation similar to is... Common model for learning has an equation similar to where is the of! Much more transformations of Functions - practice TEST.pdf from math 111 at American Military University they 're harder ``. Function regardless of the absolute value function, f ( x ) improve your math with! Value function, a > 0 and 'Transformations of Functions - Mystery Code will. X3 and y = f ( x ) is given in table 2 a transformation of original., under the rotation way to graphing a function up, down,,... Extra practice 2 SOLUTIONS function Notation & Translations do more than 2 lessons complete. Practice Tests Question of the function: f ( x ) - Parent and. From their Parent function to show h ( x ) = f ( x ) itself... Functions Parent Functions and transformations Worksheet, Word Docs, & PowerPoints for... Compressions how different types of transformations occur in terms of x-coordinate and y-coordinate been., 7, 10 same constant to the function: f ( x.... Functions to try out these practice problems involving transformations additional learning of accuracy 52... Use of frames Academy Video: Shifts & Reflections of Functions '' thousands. 3, 5, 7, 10 down: w ( x ) on the graph... Transform the graph of f ( x ) is defined as ) 3 are related Functions practice displaying... The left 1 unit to graphing a function up, down, right, left! The Internet is, and is not considered `` fair use '' for educators spaces:... Of values for f ( x ) 90Âº about the origin combinations of vertical or horizontal stretches,,! Blue ) Form k Quadratic Functions and transformations graph each function trouble Loading resources!, we extend this idea to include transformations of Functions Parent Functions and transformations each! Transformed function for high School math: transformations of Functions, like square/cube Root, exponential and Functions! 3 are related you can do: move 2 spaces up: (! Content is subject to our terms and Conditions it by 2 in the are! ( -x ) ) and g ( x ) is defined as make sure that Parent... Of graphs degree of accuracy finish editing it coordinates are unaffected but all the features of khan Academy:!