Visualize a sequence of function transformations: shifting, shrinking, stretching, and reflecting

YouTube Excerpt: Use Desmos.com to visualize transformations of functions: shifting, compression, stretching, and reflections Problem: A student wants to graph L(x) = 1 – 2(–2x + 1)^3. She wants to start with the graph of F(x) = x^3, which she knows by heart, and apply a sequence of transformations to arrive at the graph of L(x). Which transformations should she apply, and in what order? Please number your steps. Solution: Plot each transformation step at Desmos.com and observe what it does to the graph. Parent function F(x) = x^3, begin with horizontal shifting and finish with vertical shifting, if any: 1. G(x) = (x + 1)^3 [horizontal shift to the left by 1 unit (not to the right!)] 2. H(x) = (2x + 1)^3 [horizontal compression (shrinking) by a factor of 1/2 (shrink 2 times!)] 3. I(x) = (2(-x) + 1)^3 [reflection about the y-axis (not about the x-axis!)] 4. J(x) = 2(-2x + 1)^3 [vertical stretching by a factor of 2 ] 5. K(x) = -2(-2x + 1)^3 [reflection about the x-axis] 6. L(x) = -2(-2x + 1)^3 + 1 [vertical shift up by 1 unit] #Algebra #FunctionTransformations #desmos #algebrahelp Music background: Cold Funk by Kevin MacLeod | incompetech.com/ Music promoted by www.chosic.com/free-music/all/ Creative Commons CC BY 3.0 creativecommons.org/licenses/by/3.0/

Use Desmos.com to visualize transformations of functions: shifting, compression, stretching, and reflections Problem: A student wants to graph...

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