1. Scaling, translations, shift up / down and left/right
Graphing Functions
Scaling, translations, shift up / down and left/right

2. Linear functions
y = 3x + 6
It’s x to the power of 1
So it’s a straight line
And it has 1 root
y = mx + c slope y- intercept….i.e. where the line cuts the x-axis

3. Linear Functions – real life
y=12-0.5x
Height of candle depends on hours burning
Y=40x+60
Cost of plumber depends on hours worked
Y=2x-2
Number of games in league depends on number of teams
Y=3x-10
Number of ice creams sold depends on temperature outside

4. y = 2x + 3
This has a slope of 2
Also, notice where it cuts the y-axis

5. y = 2x + 4 This still has a slope of 2
Where does it cut the y-axis now?

6. y = 2x -3 This still has a slope of 2
Where does it cut the y-axis now?

7. y = 2x + 0.5 This still has a slope of 2
Where does it cut the y-axis now?

8. y = 2x
This still has a slope of 2
Where does it cut the y-axis now?

9. Student Activity
For the following LINEAR graphs, complete the equation of the LINE
Just look at the y-intercept

10. y = 2x + ??? Q1 This has a slope of 2
Also, notice where it cuts the y-axis

11. y = 2x + ??? Q2 This still has a slope of 2
Where does it cut the y-axis now?

12. y = 2x + ??? Q3 This still has a slope of 2
Where does it cut the y-axis now?

13. y = 2x + ??? Q4 This still has a slope of 2
Where does it cut the y-axis now?

14. y = 2x + ??? Q5 This still has a slope of 2
Where does it cut the y-axis now?

15. Linear functions with different slopes
y = x + 3
This has a slope of 1
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

16. Linear functions with different slopes
y = 2x + 3
This has a slope of 2
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

17. Linear functions with different slopes
y = 3x + 3
This has a slope of 3
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

18. Linear functions with different slopes
y = 4x + 3
This has a slope of 4
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

19. Linear functions with different slopes
y = 5x + 3
This has a slope of 3
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

20. Linear functions with different slopes
y = x + 3
This has a slope of 1
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Positive slope

21. Linear functions with different slopes
y = -x + 3
This has a slope of -1
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Negative slope

22. Linear functions with different slopes
y = -2x + 3
This has a slope of -2
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Negative slope

23. Linear functions with different slopes
y = -3x + 3
This has a slope of -3
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Negative slope

24. Linear functions with different slopes
y = -4x + 3
This has a slope of -4
Cuts the y-axis at 3, as before
Remember:
Slope = 𝑅𝑖𝑠𝑒 𝑅𝑢𝑛 = difference in y’s difference in x’s
Negative slope

25. Quadratic functions
y = x2

26. Quadratic functions
y = -x2

27. Quadratic functions
y = x2
This has a minimum point of (0,0)

28. Quadratic functions
y = x2 +1
This has a minimum point of (0,1)

29. Quadratic functions
y = x2 + 3
This has a minimum point of (0,3)

30. Quadratic functions
y = x2 -2
This has a minimum point of (0,-2)

31. Quadratic functions
y = x
This has a minimum point of (0,-0.5)

32. Quadratic functions
y = (x-1)2
This has a minimum point of (1,0)

33. Quadratic functions
y = (x-3)2
This has a minimum point of (3,0)

34. Quadratic functions
y = (x + 4)2
This has a minimum point of (-4,0)

35. Quadratic functions
y = (x +1.5)2
This has a minimum point of (-1.5,0)

36. Quadratic functions y = (x -2)2 - 3
This has a minimum point of (2, -3)

37. Quadratic functions y = (x - 2)2 + 3
This has a minimum point of (2, 3)

38. Quadratic functions
y = (x +2)2 -1
This has a minimum point of (2, -1)

39. Quadratic functions y = (x – 2.5)2 -0.5
This has a minimum point of (2.5, -0.5)

40. Student Activity
For the following quadratic graphs write down the equation of the curve
Just figure out how much it has moved up or down from the x-axis
And how much it has moved left or right from the origin

41. Q1
Quadratic functions
y = ………
This has a minimum point of …… ( , )

42. Q2
Quadratic functions
y = ………
This has a minimum point of …… ( , )

43. Q3
Quadratic functions
y = ………
This has a minimum point of …… ( , )

44. Q4
Quadratic functions
y = ………
This has a minimum point of …… ( , )

45. Q5
Quadratic functions
y = ………
This has a minimum point of …… ( , )

46. Q6
Quadratic functions
y = ………
This has a minimum point of …… ( , )

47. Q7
Quadratic functions
y = ………
This has a minimum point of …… ( , )

48. Q8
Quadratic functions
y = ………
This has a minimum point of …… ( , )

49. Q9
Quadratic functions
y = ………
This has a minimum point of …… ( , )

50. Q10
Quadratic functions
y = ………
This has a minimum point of …… ( , )

51. Q11
Quadratic functions
y = ………
This has a minimum point of …… ( , )

52. Quadratic functions
Q12
y = ………
This has a minimum point of …… ( , )

53. Quadratic functions
Q13
y = ………
This has a minimum point of …… ( , )

54. Quadratic functions
Q14
y = ………
This has a minimum point of …… ( , )

55. Quadratic functions
Q15
y = ………
This has a minimum point of …… ( , )

56. Exponential functions
y = 2x
This cuts the x-axis at (1,0)

57. Exponential functions
y = 2x +1
This cuts the x-axis at (2,0) ……. 1 higher

58. Exponential functions
y = 2x -3
This cuts the x-axis at (-3,0)…… 3 lower

59. Exponential functions
y = 2x
This cuts the x-axis at (1,0)

60. Exponential functions
y = 2x+1
This moves the graph 1 place to the left

61. Exponential functions
y = 2x
This cuts the x-axis at (1,0)

62. Exponential functions
y = 2x-3
This moves the graph 3 places to the right

63. See modular course worksheet – guessing which graph is which and what translation has happened to it.