Transformations of Functions

1. By: Mathew Kuruvilla 8-4 Transformations of Functions

2. Project Chapters • Intro • Slide 4 • Chapter 1: Translations of Functions • Slide 5 • Chapter 2: Vertical Stretches and Compressions of Functions • Slide 7 • Chapter 3: Horizontal Stretches and Compressions of Functions • -Slide 10

3. Intro • The first thing you need to know are the three basic types of parent functions: • f(x)=x^2 • f(x)=lxl • f(x)=√x • This is all the basic knowledge you should now for the future lesson reviews.

4. Chapter 1: Translations of Functions

5. Translating Up or Down • When you are translating up or down (vertical translation), you always have this general format in the equation if it is y=f(x): y=f(x)+k. • If 'k' is greater than 0, then the graph would be vertically translated that many spaces up. • If 'k' is less than 0, then the graph would be vertically translated that many spaces down.

6. Translating Left or Right • When you are translating left or right (horizontal translation), you always have this general format in the equation if it is y=f(x): y=f(x-h). • If 'h' is greater than 0, then the graph would be horizontally translated that many spaces to the right. • If 'h' is less than 0, then the graph would be horizontally translated that many spaces to the left.

7. The general formula of these four types of translations shown on a graph.

8. An example showing both translating up and down, and also, left and right.

9. Chapter 2: Vertical Stretches and Compressions of Functions

10. Vertical Stretch • When you are stretching (or compressing) a function vertically, the general equation for this, if it is y=f(x), would be: y=af(x) • If 'a' is greater than one in the equation, then the equation gets stretched by a factor of 'a'.

11. Vertically Compression • When you are compressing (or stretching) a function vertically, the general equation for this, if it is y=f(x), would be: y=af(x) • If 'a' is less than one and also greater than zero in the equation, then the equation gets compressed by a factor of 'a'.

12. The general formula for stretching or compressing a function vertically.

13. Examples to show how to stretch or compress a function vertically.

14. Chapter 3: Horizontal Stretches and Compressions of Functions

15. Horizontally Stretch • When you are stretching (or compressing) a function horizontally, the general equation for this, if it is y=f(x), would be: y=f(bx) • If 'b' is less than one and greater than zero in the equation, then the equation gets stretched by a factor of 1/b.

16. Horizontal Compression • When you are compressing (or stretching) a function horizontally, the general equation for this, if it is y=f(x), would be: y=f(bx) • If 'b' is greater than one in the equation, then the equation gets stretched by a factor of 1/b.

17. The general formula for stretching or compressing a function horizontally.

18. Examples to show how to stretch or compress a function horizontally.

19. Thanks for watching and Good Luck on the Midterm!!!!! (You'll really need it.....) The End