1. Transformation of Functions Section 1.6

2. Objectives Describe a transformed function given by an equation in words. Given a transformed common function, write the transformed function's equation.

3. Vocabulary common function horizontal shift vertical shift vertical stretch/shrink reflect over the x-axis reflect over the y-axis

4. Common Functions

5. Graph the functions and In general: Vertical shift up by c units

6. Graph the functions and In general: Horizontal shift left by c units

7. Graph the functions and In general: Vertical shift down by c units

8. Graph the functions and In general: Horizontal shift right by c units

9. Shift Summary Vertical shifts Horizontal shift Vertical shift up by c units Vertical shift down by c units Horizontal shift left by c units Horizontal shift right by c units

10. Graph the functions and In general: Reflect over x-axis

11. Graph the functions and In general: Reflect over y-axis

12. Graph the functions and In general: Vertical stretch away from x-axis by a factor of c

13. Graph the functions and In general: Vertical shrink toward x-axis by a factor of c

14. Graph the functions and In general: Horizontal shrink toward y-axis by a factor of 1/c

15. Graph the functions and In general: Horizontal stretch away from y-axis by a factor of 1/c

16. Stretch/Shrink/Reflection Summary Vertical Vertical shrink toward x-axis by a factor of c Vertical stretch away from x-axis by a factor of c Reflect over x-axis

17. Stretch/Shrink/Reflection Summary Horizontal Reflect over y-axis Horizontal shrink toward y-axis by a factor of 1/c Horizontal stretch away from y-axis by a factor of 1/c

18. Given, after performing the following transformations: shift to the left 76 units, shrink vertically by a factor of, and shift downward 13 units, write the new function.