Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - Transformations.
Test Yourself 1.


 

Remember when determining SHIFTS, we need to change a given equation into the form

When determining DILATIONS, we need to change a given equation into the form

Also remember that it is generally better to do the dilations before doing the shifts.

 

Shift only 1. What is the new equation when
y = x2 is shifted 2 units to the left?		 2. What is the new equation when
y = x3 is shifted 3 units to the right?
  3. What is the new equation when
y = 5x is shifted 5 units down?		 4. What is the new equation when
y = x - 5 is shifted 2 units up?
  5. What is the new equation when
y = 5x2 + 2 is shifted 3 units to the left?		 6. What is the new equation when
y = 2√x - 2.6 is shifted 0.5 units up?
  7. What is the new equation when
y = 5 is shifted 6 units down?		 8. What is the new equation when
x = -4 is shifted 2 units to the right?
Dilation only 9. What is the new equation when
y = x2 is dilated vertically by a factor of 2?		 10. What is the new equation when
y = 2x is dilated vertically by a factor of 1/3?
  11. What is the new equation when
is dilated horizontally by a factor of 3?		 12. What is the new equation when
y = x2 is dilated horizontally by a factor of 0.5?
  13. What is the new equation when
y = (x - 1)(x + 2) is dilated horizontally by a factor of 3?		 14. What is the new equation when
y = (x - 1)(x + 2) is dilated vertically by a factor of 3?
Identify the shift 15. What is the shift when y = 2x2 + 1 changes to y = 2x2 - 3? 16. What is the shift when y = 4x3 changes to y = 4 (x + 2)3?
  17. What shifts were made to change
y = x2 + y2 to y = (x + 1)2 + (y - 2)2?		 18. What shift was made to change
y = sin x to y = sin (x - π)?
Identify the dilation 19. What dilation factor was applied to y = 2x2 to transform it to y = 4x2?

What is the effect?

 20. What dilation factor was applied to
y = 3 cos x to transform it to y = cos x?

What is the effect?
  21. What dilation factor was applied to
y = 2x to transform it to y = 2x+2?

What is the effect?

 22. What dilation factor was applied to
y = 2x + 4 to transform it to y = x + 2?

What is the effect?
Shift and dilation 23. What are the transformations required to change x2 + y2 = 4

into (x - 3)2 + (y + 4)2=16

 24. What transformation(s) must be applied to change x2 + y2 = 1 into
?
  25. What are the transformations required to change y = cos x into
y = 5cos(2x - π/3)		 26. Starting with the equation

what transformations change the equation to

?
  27. Starting with the equation

what transformations change the equation to

?

 28. Starting with the equation

what transformations change the equation to

?
 

29. Use the following diagram of y = f(x) = x2 to sketch new graphs in response to the information given in each of questions 29-30.
  30. Sketch 30. Sketch .
Diagrams

31. Use the following diagram of y = f(x) to sketch new graphs in response to the information given in each of parts (i) - (iv).

(i) Sketch y = f(x + 1).

(ii) Sketch y = 1 + f(x + 2)

(iii) Sketch y = 1 + 2f(x)

(iv) Sketch y = 2f(2x)
 

32. Reflect the shape ABCDE about the line PQ.

 33.
  34. 35.