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Exploring Graph Transformations: Reflections, Translations, and Dilations Explained

Master the art of graph transformations with this comprehensive guide. Learn about basic graphs including identity, squaring, cubing, reciprocal, absolute value, and square root. Discover how to reflect, translate, and dilate functions using simple rules and the Desmos app. Engage with interactive tools to visualize transformations of functions. By working through practical examples and hands-on exercises, you'll gain a firm grasp on how various transformations impact the graph's appearance. Ideal for students and educators looking to deepen their understanding of graphing concepts.

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Exploring Graph Transformations: Reflections, Translations, and Dilations Explained

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  1. 2.2 Reflections & Transformations

  2. We need to have a firm grasp on our basic graphs, so we can then easily transform them using some simple rules. 6 Basic Graphs: (1) Identity (2) Squaring (3) Cubing (6) Reciprocal Absolute Value Square Root

  3. 3 ways to change up a graph – Reflections, Translations, & Dilation Start with y = f (x) Reflections Translations y = f (x – c) + d shift

  4. Dilations stretch or compress y = af(x) Let’s Explore! iPad app Desmos (can also access online @ desmos.com ) Start Desmos Find button in top left corner Choose transformations  Reflections of a function Explore this graph! touch next to the 5 & delete up to = enter your own change box 4 to x = f (y) (use ABC) touching next to the next to the formula will “turn on” each graph Are they what you expected? Launch website

  5. Launch website Now let’s explore translations Go to , under Transformations  Translating Any Function delete function in box 1 go to    put x in ( ) Play with h & k put in negative values/ positive values use slider or enter a # in boxes 5 & 7 or change values in equation directly in box 3

  6. Launch website Time for Dilations Go to , under Transformations  Scaling Any Function delete function in box 1 type in x2 Play with a  make bigger or smaller – use slider or type in #s Bring it all together! Describe (yes, write a sentence!) how the basic graph of y = x3 has been changed Then check on Desmos or calculator Touch & Type in the equation & confirm your description! y = 2 (x + 3)3 – 2 Graph

  7. Homework #202 Pg 69 #1–43 odd, 38, 40, 42, 44

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