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