For example, consider the functions g ( x ) = x 2 − 3 and h ( x ) = x 2 + 3. If we add a negative constant, the graph will shift down. If we add a positive constant to each y-coordinate, the graph will shift up. This occurs when a constant is added to any function. is a rigid transformation that shifts a graph up or down relative to the original graph. changes the size and/or shape of the graph.Ī vertical translation A rigid transformation that shifts a graph up or down. A non-rigid transformation A set of operations that change the size and/or shape of a graph in a coordinate plane. changes the location of the function in a coordinate plane, but leaves the size and shape of the graph unchanged. A rigid transformation A set of operations that change the location of a graph in a coordinate plane but leave the size and shape unchanged. When the graph of a function is changed in appearance and/or location we call it a transformation. GRAPH TRANSFORMATIONS ZIP FILEzip file containing this book to use offline, simply click here. You can browse or download additional books there. More information is available on this project's attribution page.įor more information on the source of this book, or why it is available for free, please see the project's home page. Additionally, per the publisher's request, their name has been removed in some passages. However, the publisher has asked for the customary Creative Commons attribution to the original publisher, authors, title, and book URI to be removed. Normally, the author and publisher would be credited here. This content was accessible as of December 29, 2012, and it was downloaded then by Andy Schmitz in an effort to preserve the availability of this book. GRAPH TRANSFORMATIONS LICENSESee the license for more details, but that basically means you can share this book as long as you credit the author (but see below), don't make money from it, and do make it available to everyone else under the same terms. GRAPH TRANSFORMATIONS SERIESThe final exercise asks students to solve a series of quadratic equations.This book is licensed under a Creative Commons by-nc-sa 3.0 license. This is followed by pages of notes explaining the nature of quadratic equations including the formula for solving quadratic equations, the determinant, factorising a quadratic and completing the square. The fourth activity explores the roots of a quadratic equation. The third activity asks students to form equations to match the paths shown on the screen. The second activity requires students to change the values of a, b and c so that the green graph matches the blue graph on the screen. There follows an explanation of the first task in which students have to investigate how changing the coefficients a, b and c in the function f(x) =a(x+b)2+c affect the graph. This interactive resource is designed to enable students to explore what is meant by a quadratic equation, the meaning of the coefficients of a quadratic equation and to be able to solve quadratic equations.Īn introduction page gives examples of where quadratic equations can be found which is useful for class discussion. Quality Assured Category: Mathematics Publisher: University of Leicester GRAPH TRANSFORMATIONS HOW TOThe resource includes teacher notes with guidance on teaching strategies and how to model examples for students. Extension suggestions are to work with general equations, trigonometric equations and to explore reflections in the x axis and reflections in the y axis. It is recommended that students begin their investigation with linear functions, quadratic functions and a reciprocal function. Students are required to explore different transformations, record their results on the sheet and use their results to generalise the effect of each transformation. Ideally students should have access to appropriate graph plotting technology to investigate the tasks. stretch parallel to the x axis from the y axis.stretch parallel to the y axis from the x axis,.
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