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One way to think of end behavior is that for \(\displaystyle x\to -\infty \), we look at whats going on with the \(y\) on the left-hand side of the graph, and for \(\displaystyle x\to \infty \), we look at whats happening with \(y\) on the right-hand side of the graph. Even and odd functions: Graphs and tables, Level up on the above skills and collect up to 320 Mastery points, Level up on the above skills and collect up to 240 Mastery points, Transforming exponential graphs (example 2), Graphical relationship between 2 and log(x), Graphing logarithmic functions (example 1), Graphing logarithmic functions (example 2). 12. Sample Problem 2: Given the parent function and a description of the transformation, write the equation of the transformed function!". About the author: Tom Reardon taught every math course at Fitch High School (Ohio) during his 35-year career, where he received the Presidential Award and attained National Board Certification. b. c. d. 16. g(x) = |x+3|? and transformations of the cubic function. \(x\) changes:\(\displaystyle f\left( {\color{blue}{{\underline{{\left| x \right|+1}}}}} \right)-2\): Note that this transformation moves down by 2, and left 1. Try the free Mathway calculator and 13. These are the things that we are doing vertically, or to the \(y\). \(\displaystyle f\left( {-\frac{1}{2}\left( {x-1} \right)} \right)-3\), \(\displaystyle f\left( {-\frac{1}{2}\left( {x-1} \right)} \right)\color{blue}{{-\text{ }3}}\), \(\displaystyle f\left( {\color{blue}{{-\frac{1}{2}}}\left( {x\text{ }\color{blue}{{-\text{ }1}}} \right)} \right)-3\), \(\displaystyle f\left( {\left| x \right|+1} \right)-2\), \(\displaystyle f\left( {\left| x \right|+1} \right)\color{blue}{{\underline{{-\text{ }2}}}}\). Click on Submit (the blue arrow to the right of the problem) and click on Describe the Transformationto see the answer. Transformations of functions | Algebra 2 | Math | Khan Academy Now to write the function, I subject the expression to successive transformations in the order listed above. ACT is a registered trademark of ACT, Inc. (we do the opposite math with the \(x\)), Domain: \(\left[ {-9,9} \right]\) Range:\(\left[ {-10,2} \right]\), Transformation:\(\displaystyle f\left( {\left| x \right|+1} \right)-2\), \(y\) changes: \(\displaystyle f\left( {\left| x \right|+1} \right)\color{blue}{{\underline{{-\text{ }2}}}}\). y = x3 (cubic) Then you would perform the \(\boldsymbol{y}\) (vertical) changes the regular way: reflect and stretch by 3 first, and then shift up 10. Transformation: \(\displaystyle f\left( {-\frac{1}{2}\left( {x-1} \right)} \right)-3\), \(y\)changes:\(\displaystyle f\left( {-\frac{1}{2}\left( {x-1} \right)} \right)\color{blue}{{-\text{ }3}}\), \(x\) changes:\(\displaystyle f\left( {\color{blue}{{-\frac{1}{2}}}\left( {x\text{ }\color{blue}{{-\text{ }1}}} \right)} \right)-3\). Top Tips From a Science Teacher for Taking AP Exams in 2023, Earth Day Engineering: Mr. Trash Wheel and More Classroom-Ready Activities To Use With Your Students, 5 Study Tips from a Student #StudyGrammer, Math in Motion 5 Educators Using Robotics To Teach Math, Leveraging CAS To Explore & Teach Mathematics, Part 2, Puzzling Students to Push Their Understanding, TIs Path to STEM Projects Are Now Available in Python, Field Goal vs. Ice Cream: The Ultimate Game Day Matchup, Math and Python: A Great Valentines Day Couple, Top Tips From a Science Teacher for Taking AP Exams in 2022, Mission Impossible: A Perfect March Madness Bracket, Expanding Your Wealth of Knowledge Through Financial Literacy, Get Your Promposal Ready Try Balloons and Buttons.