1. Transforming functions

2. Learning objectives
Translate functions left and right left = f(x+…), right = f(x-…)
Translate functions up and down up = f(x)+…, down = f(x)-…
Stretch functions parallel to y-axis 2f(x), ½f(x) etc.
Stretch functions parallel to x-axis f(2x), f(½x) etc.

3. f(x)
f(x) = x2 – 4 x
f(-2) = (-2)2 – 4 = 0
f(2) = 22 – 4 = 0
f(-1) = (-1)2 – 4 = -3
f(1) = (1)2 – 4 = -3
f(0) = 02 – 4 = -4

4. Drawing 2f(x) … f(x) f(x) = x2 – 4 x 2f(-2) = 20 = 0
Stretch x2 away from the x-axis (Double y coordinates)
2f(0) = 2(-4) = -8

5. Drawing ½f(x) … f(x) f(x) = x2 – 4 x ½f(-2) = ½0 = 0
Squash by ½ towards the x-axis (Halve y coordinates)

6. ( ) Drawing f(x)+3 … f(2)+3 = 0+3 = 3 f(x) f(-2)+3 = 0+3 = 3 x
f(x) = x2 – 4
( )
Translate 0 3

7. ( ) Drawing f(x+3) … f(-1+3) = f(2) = 0 f(x) f(-5+3) = f(-2) = 0
f(x) = x2 – 4 x
f(-4+3) = f(-1) = -3
f(-2+3) = f(1) = -3
f(-3+3) = f(0) = -4
( )
Translate -3

8. ( ) Drawing f(x)-1 … f(x) f(x) = x2 – 4 x f(-2)-1 = 0-1 = -1
( )
Translate 0 -1

9. ( ) Drawing f(x-1) … f(x) f(3-1) = f(2) = 0 f(-1-1) = f(-2) = 0 x
f(x) = x2 – 4
f(1-1) = f(0) = -4
( )
Translate 1

10. Drawing f(2x) … f(x) f(x) = x2 – 4 x
Squash by ½ towards the y-axis (Halve x coordinates)

11. Drawing f(½x) … f(x) f(x) = x2 – 4 x
Stretch x2 away from the y-axis (Double x coordinates)

12. Recap learning objectives
Translate functions left and right left = f(x+…), right = f(x-…)
Translate functions up and down up = f(x)+…, down = f(x)-…

13. Recap learning objectives
Stretch functions parallel to y-axis 2f(x), ½f(x) etc.
Stretch functions parallel to x-axis f(2x), f(½x) etc.
And finally …

14. f(-x) … Reflection in y-axis
Drawing f(-x) …
f(x)
f(-x) … Reflection in y-axis

15. -f(x) … Reflection in x-axis
Drawing -f(x) …
f(x)
-f(x) … Reflection in x-axis

16. -f(-x) … Rotation 180° about (0,0)
Drawing -f(-x) …
f(x)
-f(-x) … Rotation 180° about (0,0)