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Non-Rigid Graphical Transformations in Precalculus

Explore non-rigid graphical transformations without a calculator. Learn about vertical and horizontal stretching, shrinking, and reflections. Practice with examples and homework to reinforce concepts. Quiz upcoming on October 2.

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Non-Rigid Graphical Transformations in Precalculus

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  1. Today in Precalculus • Do NOT need a calculator • Go over homework • Notes: Non-Rigid Graphical Transformations • Homework

  2. Non-Rigid Transformations • Changes the size and shape of the graph. • Types: • Stretches • Shrinks • Can be vertical or horizontal

  3. Vertical • Multiply equation by a factor c: y = c∙f(x) • If c > 1, stretch by a factor of c • If c < 1, shrink by a factor of c y=x3-5x y=1/2(x3-5x)

  4. Horizontal • Divide the x in the function by c: • If c > 1, stretch by a factor of c • If c < 1, shrink by a factor of c y=x3-5x y=(x/.5)3-5(x/.5)

  5. Misc • Reflections: If c is negative in either the vertical or horizontal stretch/shrink, the graph reflects and stretches/shrinks. • Order matters when combining transformations • Stretch/shrink • Reflections • Shifts

  6. Example Basic function: x2 Key points: (0,0), (1,1), (-1,1) Vertical stretch 3 (multiply y by 3) Down 4

  7. Example Basic function: x3 Key points: (0,0), (1,1), (-1,-1) Reflect over x-axis Vertical stretch 1/2 (multiply y by 1/2) Right 3

  8. Example b. y = 0.5f(x + 1) – 2 c. y = f(x – 2) + 3

  9. Homework • Pg 147: 13-16, 21, 24, 26, 39, 43, 44, 47, 49, 51-54 • Memorize 10 basic functions • Quiz Friday, October 2

  10. Homework 2) up 5.2 4) Right 3 6) Down 100 8)Left 50 down 279 10)Right 5 18)Reflect over x-axis, left 4 30)

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