Transformationss
- 1. Homework Dilemma.. Captain Jabbamathee to the rescue! homework – by flickr user bjortklingd
- 2. Question #1 Given y = f(x) Graph y = |f(x)| - 2
- 3. Step 1: Absolute Value Find the absolute value of f(x) This means, that the graph cannot have negative “y” coordinates
- 4. Step 2: Transformation Move the graph 2 units down This shows the transformation of the graph
- 5. Question #2 Given y = f(x), sketch the following function Sketch y = -2f(1/2x – 2) + 3 Rewrite equation to factor out ½ y = -2f1/2(x – 4) + 3 Which transformation comes 1 st , 2 nd , 3 rd and 4 th ? 1 st vertical stretch 2 nd horizontal compression 3 rd horizontal shift 4 th vertical shift -2 ½ -4 3
- 6. y = -2f1/2(x – 4) + 3 The –2 corresponds to the “y” value and the ½ corresponds to the “x” values The coordinates in the function y = f(x) will change so that all the “x” values will be multiplied by 2 and all of the “y” values will be multiplied by –2 (vertical stretch and horizontal compression) (-2,0) (-1, 2) (0, 0) (2, 0) (2, 2) (3, 2) (-4, 0) (-2, -4) (0, 0) (4, 0) (4, -4) (6, -4)
- 7. Equation: y = -2f1/2(x – 4) + 3 The –4 slides the graph so that it moves 4 units to the right, however if it was (x + 4), the graph would move 4 units to the left The 3 would move the graph 3 units up (horizontal and vertical shift) (-4, 0) (-2, -4) (0, 0) (4, 0) (4, -4) (6, -4) ( 0, 3) (2, -1) (4, 3) (8, 3) (8, -1) (10, -1) *note: remember stretches before translations*