1. Transformation of Graphs
Andrew Robertson

2. Transformation of f(x)+a
f(x) = x2

3. Transformation of f(x)+a
y = x2 + 3

4. Transformation of f(x)+s
y = x2 - 2

5. Transformation of sf(x)
f(x) = (x-2)(x-3)(x+1)
2f(x)

6. Transformation of sf(x)
y=2f(x) = 2(x-2)(x-3)(x+1)
0.5f(x)

7. Transformation of sf(x)
y=0.5f(x) = 0.5(x-2)(x-3)(x+1)

8. Transformation of f(x+s)
f(x) = x2
f(x-2)

9. Transformation of f(x+s)
y=f(x-2) = (x-2)2
f(x+2)

10. Transformation of f(x+s)
y=f(x+2) = (x+2)2

11. Transformation of f(sx)
f(x) = (x-2)(x-3)(x+1)
f(2x)

12. Transformation of f(sx)
y=f(2x) = (2x-2)(2x-3)(2x+1)
f(0.5x)

13. Transformation of f(sx)
y=f(0.5x) = (0.5x-2)(0.5x-3)(0.5x+1)
-f(x)

14. Transformation of -f(x)
f(x) = (x-2)(x-3)(x+1)
-f(x)

15. Transformation of -f(x)
y=-f(x) = -[(x-2)(x-3)(x+1)]
f(-x)

16. Transformation of f(-x)
f(x)=(x-2)(x-3)(x+1) y=f(-x)=(-x-2)(-x-3)(-x+1)

17. Combinations of transformations
f(x)= x2 then y=f(x+2)-3 = (x+2)2 -3

18. Combinations of transformations
y = x2 then y=-2f(x-3) = -2(x-3)2

19. F(αx±β) - Inside brackets always effects the horizontal
αF(x) ±β - Outside brackets always effects the vertical

20. f(x) ± a Vertical shift (x,y) -> (x, y ± a)
f(x ± a) Horizontal shift (x,y) -> (x a, y)
Note that when + shift to Left and – shift to Right
αf(x) Vertical Stretch/compression by factor α
(x,y) -> (x, αy)
f(αx) Horizontal Stretch/compression by factor 1/α
(x,y) -> (x/α, y)
f(-x) Refection though y axes (x,y)  (-x, y)
- f( x) Reflection through x axes (x,y)  ( x, -y)