1. Transforming curves www.teachitmaths.co.uk 2015167891

2. A: y = f(x) + 2 B: y = f(x) - 2 C: y = f(x + 2) D: y = f(x - 2) A 1 The red curve has equation y = f(x) What is the equation of the blue curve? Explanation © www.teachitmaths.co.uk 2015167892

3. A: y = f(x) + 2 A 1 Explanation y = f(x) + a translates f(x) by a units in the y direction. +a moves it up, -a moves it down. y = f(x) y = f(x) + 2 www.teachitmaths.co.uk 2015167893

4. A: y = f(x) + 2 B: y = f(x) - 2 C: y = f(x + 2) D: y = f(x - 2) D 2 The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 2015167894 Explanation

5. D: y = f(x - 2) D 2 Explanation y = f(x - a) translates f(x) by a units in the x direction. +a moves it left, -a moves it to the right. y = f(x) y = f(x–2) www.teachitmaths.co.uk 2015167895

6. A: y = f(2x) B: y = ½f(x) C: y = 2f(x) D: y = f(½x) C 3 The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 2015167896 Explanation

7. C: y = 2f(x) C 3 Explanation y = af(x) stretches f(x) parallel to the y-axis with a scale factor of a. x coordinates are the same but y coordinates are multiplied by a. y = f(x) y = 2f(x) www.teachitmaths.co.uk 2015167897

8. A: y = -f(x) B: y = f(-x) C: y = f(x + 1) D: none of the above B 4 The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 2015167898 Explanation

9. B: y = f(-x) B 4 Explanation y = f(–x) is a reflection of y = f(x) in the y-axis. y = f(x) y = f(–x) www.teachitmaths.co.uk 2015167899

10. 5 A: y = f(2x) B: y = ½f(x) C: y = 2f(x) D: y = f(½x) D The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678910 Explanation

11. D: y = f(½x) 5 D y = f(x) y = f(½x) www.teachitmaths.co.uk 20151678911

12. A: y = -f(x) B: y = f(-x) C: y = f(x + 1) D: none of the above A 6 The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678912 Explanation

13. A: y = -f(x) A 6 Explanation y = -f(x) is a reflection of y = f(x) in the x-axis. y = f(x) y = -f(x) www.teachitmaths.co.uk 20151678913

14. A: y = f(x) + 2 B: y = f(x) - 2 C: y = 4 - f(x) D: y = 4 + f(-x) C 7 (0,1) (0,3) The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678914 Explanation

15. C: y = 4 - f(x) C 7 (0,1) (0,3) Explanation y = a - f(x) is a combination of transformations: a reflection in the x-axis and a translation a in the positive y direction. y = f(x) y = 4 - f(x) www.teachitmaths.co.uk 20151678915

16. A: y = f(-x) + 8 B: y = f(8 - x) C: y = f(2 - x) D: y = f(x + 2) C 8 (3,0)(-5,0) The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678916 Explanation

17. C: y = f(2 - x) C 8 (3,0)(-5,0) Explanation y = f(a - x) is a combination of transformations: a reflection in the y-axis and a translation a in the negative x direction. y = f(x) y = f(2-x) www.teachitmaths.co.uk 20151678917

18. A: y = -f(x) B: y = f(-x) C: y = -f(-x) D: none of the above D 9 (-2,-4) (-2,4) The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678918 Explanation

19. D: y = none of the above D 9 (-2,-4) (-2,4) Explanation The transformation of y = f(x) is by a reflection in the x-axis and then another in the y-axis but also includes a translation. y = f(x) y = -f(x) gives a reflection in the x-axis only. y = f(-x) gives a reflection in the y-axis only. y = -f(-x) gives a reflection in both the x-axis and y-axis but no translation. www.teachitmaths.co.uk 20151678919

20. A: y = f(x + 2) + 3 B: y = f(x - 2) + 3 C: y = f(x + 3) + 2 D: y = f(2 - x) + 3 A 10 (-4,7) (-2,4) The red curve has equation y = f(x) What is the equation of the blue curve? www.teachitmaths.co.uk 20151678920 Explanation

21. A: y = f(x + 2) + 3 A 10 (-4,7) (-2,4) Explanation y = f(x + a) + b is a combination of transformations: y = f(x) y = f(x+2) + 3 translation a in the negative x direction and b in the positive y direction. www.teachitmaths.co.uk 20151678921