1. 2.5 Transformations and Combinations of Functions

2. Vertical Shift Up Y=f(x) Y=f(x)+c

3. Vertical Shift Down Y=f(x) Y=f(x)-c

4. Horizontal Shift to the Left Y=f(x) Y=f(x+c)

5. Horizontal Shift to the Right Y=f(x) Y=f(x-c)

6. Study Tip We know that positive numbers are to the right of zero on a number line and negative numbers are to the left of zero. This positive-negative orientation does not apply to horizontal shifts. A positive number causes a shift to the left and a negative number causes a shift to the right.

7. Reflection About the x-Axis Y=f(x) Y=-f(x)

8. Reflection About the y-Axis Y=f(x) Y=f(-x)

9. Vertical Stretching and Shrinking Graphs

10. Y=f(x) Y=1/2f(x) Y=2f(x)

11. Summary of Transformations c represents a positive real number.

16. The Sum of Functions

17. The Difference of Functions

18. The Product of Functions

19. The Quotient of Functions