1. Translation

2. In mathematics, a translation moves a shape in a straight line.

3. . The resulting shape. (image) is congruent to
 The resulting shape (image) is congruent to the original; it just moves.

4. T(x,y) = (x + h, y + k) is a translation that moves the figure h units horizontally and k units vertically h over and k up

5. What translation is shown?

6. T(x,y) = (x + 6 , y – 2)

7. Translating Graphs

8. Vertical Translations The function y = f(x) + k is the same as y = f(x), but has a vertical translation of k.

9. Vertical Translations The functions shown are y = | x | y = | x | + 10 y = | x | – 10

10. So … A number at the end of an equation moves the graph up or down that number.

12. Horizontal Translations The function y = f(x – h) is the same as y = f(x), but has a vertical translation of h.

13. Horizontal Translations The functions shown are y = | x | y = | x – 10 | … blue y = | x + 10 | … red

14. Important … horizontal translations move the opposite direction of the number in the equation.

15. So … A number in parentheses moves the graph left or right the opposite of that number.

17. So y = (x – h)2 + k is a translation equivalent to T(x,y) = (x + h, y + k)

18. What would the graph of y = (x + 4)2 – 5 look like?

19. What would the graph of y = (x + 4)2 – 5 look like. 
What would the graph of y = (x + 4)2 – 5 look like?  Quadratic  parabola  Moves 5 down  Moves 4 to the left

20. What would the graph of y = (x + 4)2 – 5 look like?  4 left, 5 down

21. What would the graph of y = | x – 1 | + 3 look like?

22. What would the graph of y = | x – 1 | + 3 look like. 
What would the graph of y = | x – 1 | + 3 look like?  Absolute value  V  Moves 3 up  Moves 1 to the right

23. What would the graph of y = | x – 1 | + 3 look like? 1 right, 3 up

24. What function is f(x)? … h(x)?

25. What function is f(x). … h(x)
What function is f(x)? … h(x)? Both are square roots f(x) moves left 1, not up/down

26. What function is f(x)? … h(x)? _____ f(x) =  x + 1

27. What function is f(x)? … h(x)? h(x) moves left 3 and down 4

28. What function is f(x). … h(x)
What function is f(x)? … h(x)? h(x) moves left 3 and down 4 _____  x – 4

29. Note … to avoid confusion _____  x + 3 – 4 is often written as _____ -4 +  x + 3

30. What function is shown?

31. What function is shown? Greatest integer Moved 1 to the left

32. What function is shown? Greatest integer Moved 1 to the left y = |x + 1|

33. What function is shown?

34. What function is shown? Cubic function Moved 3 up

35. What function is shown? Cubic function Moved 3 up y = x3 + 3