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2.2 Reflections & Transformations

Learn how to transform basic graphs using simple rules such as reflections, translations, and dilations. Explore these concepts using the Desmos app on iPad or online.

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2.2 Reflections & Transformations

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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  Inverse of a function Explore this graph! touch next to the 5 in box 1 & 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 up to = 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 up to = 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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