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Rigid Transformations in Precalculus: Homework and Notes on Graphical Transformations (100 characters)

This lesson covers rigid graphical transformations in precalculus, including vertical and horizontal shifts, reflections, and their impact on equations. Homework assignments and practice examples are provided. (498 characters)

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Rigid Transformations in Precalculus: Homework and Notes on Graphical Transformations (100 characters)

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  1. Today in Precalculus • Need a calculator • Go over homework • Notes: Rigid Graphical Transformations • Homework

  2. Rigid Transformations • Leave the size and shape of the graph unchanged. • Types: • vertical shifts • horizontal shifts • reflections

  3. Vertical Translations • Shift the graph up and down • Equation is changed by simply adding or subtracting a constant. y = f(x) + c or y = f(x) – c y=x2+3 y=x2 y=x2-2

  4. Horizontal Translations • Shift the graph left and right • Equation is changed by adding or subtracting a constant from x. (moves in opposite direction) y = f(x+c) or y = f(x-c) y=(x-2)2 y=(x+3)2 y=x2

  5. Practice • A cosine graph with a vertical shift down 5 • An absolute value graph with a horizontal shift left 2 • A parabola with a vertical shift up 4 and a horizontal shift left 3 y = (x+3)2 + 4 y = cos(x) – 5 y = |x+2|

  6. Reflections • Two graphs that are symmetric with respect to a line (such as the x- or y-axis) • To reflect across the x-axis negate the entire function y = –f(x) • To reflect across the y-axis, negate every x within the function y = f(–x)

  7. Example

  8. Misc. • What happens when an even function is reflected across the y-axis? • Identical graphs • What happens when an odd function is reflected across the x- versus the y-axis? • Reflections are identical

  9. Homework • Pg 147: 2-10 even, 17-19 all, 25, 27, 29, 30 • Memorize 10 basic functions • Quiz Friday

  10. Homework answers 2) G 4) A 6) F 8) H 10) C 12) B

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