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

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

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

4. 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=x 2 y=x 2 +3 y=x 2 -2

5. 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 y=(x-2) 2 y=(x+3) 2

6. 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 = cos(x) – 5 y = |x+2| y = (x+3) 2 + 4

7. 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)

8. Example

9. Misc. What happens when an even function is reflected across the y-axis? –Identical graphs What happens when an odd function is reflected across both the x- and y-axis? –Reflections are identical

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