1. Lake Zurich High School
Parent Graphs
with translations
By: Jeffrey Bivin
Lake Zurich High School
Last Updated: November 21, 2005

2. y =|x|
Jeff Bivin -- LZHS

3. y = |x+1| + 2
x+1 = 0
x = -1 2 1
Jeff Bivin -- LZHS

4. y = |2x+5| - 4 2x+5 = 0 x = -(5/2) 4 5/2 squeeze squeeze Slope: -2
Jeff Bivin -- LZHS

5. y = 2 |x - 3| + 1 x - 3 = 0 x = 3 1 3 stretch stretch Slope: 2
Jeff Bivin -- LZHS

6. y = 3 |2x - 3| - 4 2x - 3 = 0 x = 3/2 4 stretch stretch 3/2 squeeze
Slope: -3(2) = -6
Slope: 3(2) = 6
Jeff Bivin -- LZHS

7. y = [ x ] x = 0 1 1 Note: y = x Length = 1/1 = 1 Start: (0, 0)
Height = 1
Note:
y = x
Jeff Bivin -- LZHS

8. y = [ x+1] + 2 x+1 = 0 1 1 x = -1 1 2 Note: y = (x + 1) + 2 y = x + 3
Length = 1/1 = 1 1
Start: (-1, 2)
Height = 1 2
Note:
y = (x + 1) + 2
y = x + 3
Jeff Bivin -- LZHS

9. y = 3[(½)x] stretch stretch stretch stretch Note: y = 3( (1/2)x )
Length = 1/(1/2) = 2
stretch
stretch
Height = 3
Start: (0, 0)
stretch
stretch
Note:
y = 3( (1/2)x )
y = (3/2)x
Jeff Bivin -- LZHS

10. y = -2[ x+1]+3 1 x+1 = 0 x = -1 1 stretch stretch 3 Note:
Length = 1/1 = 1
Start: (-1, 3) 1
Height = -2
stretch
stretch 3
Note:
y = -2(x + 1) + 3
y = -2x + 1
Jeff Bivin -- LZHS

11. y = [ |x| ]
Jeff Bivin -- LZHS

12. y = | [x] |
y = [ x ]
Jeff Bivin -- LZHS

13. y = | [x] |
y = | x |
Jeff Bivin -- LZHS

14. f(x) = x2
Jeff Bivin -- LZHS

15. f(x) = (x - 3)2 + 1
x - 3 = 0
x = 3 3 1
Jeff Bivin -- LZHS

16. f(x) = (x + 2)2 - 4
x + 2 = 0
x = -2 2 4
Jeff Bivin -- LZHS

17. f(x) = 2(x - 3)2 - 1 x - 3 = 0 x = 3 3 1 stretch stretch
Jeff Bivin -- LZHS

18. Jeff Bivin -- LZHS

19. x - 2 = 0
x = 2 3 2
Jeff Bivin -- LZHS

20. x + 3 = 0
x = -3 3 4
Jeff Bivin -- LZHS

21. f(x) = x3
Jeff Bivin -- LZHS

22. f(x) = (x-4)3 - 2
x - 4 = 0
x = 4 4 2
Jeff Bivin -- LZHS

23. f(x) = -(x + 2)3 -1
x + 2 = 0
flip
x = -2 2 1
Jeff Bivin -- LZHS

24. Jeff Bivin -- LZHS

25. x - 4 = 0
x = 4
y = 2 4 2
x = 4
Jeff Bivin -- LZHS

26. x + 2 = 0
y = 3
x = -2 2 3
x = -2
Jeff Bivin -- LZHS

27. flip
x - 3 = 0
x = 3
y = 1 3 1
x = 3
Jeff Bivin -- LZHS

28. f(x) = 2x
Jeff Bivin -- LZHS

29. f(x) = 2x-3
x - 3 = 0
x = 3
(3, 1) 3
Jeff Bivin -- LZHS

30. f(x) = 2x+2 - 3 x + 2 = 0 x = -2 3 2 y = -3 (-2, -2)
Jeff Bivin -- LZHS

31. f(x) = 2-x
(0, 1)
Jeff Bivin -- LZHS

32. f(x) = -(2)-x+4 – 2 -x + 4 = 0 x = 4 4 2 y = -2 flip (4, -3)
Jeff Bivin -- LZHS

33. y = g(x)
Jeff Bivin -- LZHS

34. y = g(x-3) - 2
x - 3 = 0
x = 3 3 2
Jeff Bivin -- LZHS