1 / 69

Basic Skills in Higher Mathematics

Basic Skills in Higher Mathematics. Mathematics 1(H) Outcome 2. Robert Glen Adviser in Mathematics. Mathematics 1(Higher). Outcome 2 Associate functions and graphs. y. Functions and graphs. x. Mathematics 1(Higher). Outcome 2 Associate functions and graphs. y. PC Index.

Download Presentation

Basic Skills in Higher Mathematics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Basic Skills in Higher Mathematics Mathematics 1(H)Outcome 2 Robert GlenAdviser in Mathematics

  2. Mathematics 1(Higher) Outcome 2 Associate functions and graphs y Functions and graphs x

  3. Mathematics 1(Higher) Outcome 2 Associate functions and graphs y PC Index Click on the one you want PC(a) Related functions and graphs x PC(b) Exponential and logarithmic graphs PC(c) Composite functions

  4. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Related functions and graphs

  5. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Index Click on the one you want 1 y = f (x)  a Slide up/down 2y = f (x a) Slide left/right 3y = -f (x) Reflect in x-axis 4y = f (-x) Reflect in y-axis 5y = kf (x) Stretch/compress vertically 6 y = f (kx) Stretch/compress horizontally

  6. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 1 y = f (x)  a Slide up/down

  7. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs  In this graph every point on y = f(x) has moved up 5 units. y y = f (x) + 5  +5   y = f (x) 5 +5 +5 -2  In this graph every point on y = f(x) has moved down 2 units. y = f (x) - 2   -2 -2  0  x -2

  8. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs In this graph every point on y = f(x) has moved up aunits. y y = f (x) + a y = f (x) In this graph every point on y = f(x) has moved down bunits. +a y = f (x) - b x -b

  9. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for each graph. y a y = x2 3 Here are the answers b 0 x a y = x2 + 3 -1 b y = x2 - 1

  10. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for each graph. y a 9 y = x3 - 5x 0 x Here are the answers a y = x3 - 5x +9 b -8 b y = x3 - 5x - 8

  11. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for each graph. y a 8 6 4 y = f (x) 2 0 x Here are the answers -2 b -4 a y = f (x) + 4 -6 b y = f (x) - 6

  12. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 1 Continue with Section 2

  13. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 2 y = f (x a)Slide left/right

  14. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y In this graph every point on y = f(x) has moved 5 units to the left. In this graph every point on y = f(x) has moved 3 units to the right. -5 +3    +3 -5    Notef (x+ 5) moves the graph -5. Notef (x- 3) moves the graph +3. -5 +3    x -5 3 0 y = f (x - 3) y = f (x + 5) y = f (x)

  15. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y In this graph every point on y = f(x) has moved aunits to the left. In this graph every point on y = f(x) has moved bunits to the right. Notef (x+a) moves the graph -a. Notef (x-b) moves the graph +b. x 0 -a +b y = f (x - b) y = f (x + a) y = f (x)

  16. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for each graph. Click the mouse to see the answers. y b a x 0 -5 3 y =(x + 5)2 y =(x - 3)2 y = x2

  17. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for each graph. Click the mouse to see the answers. y a b x 0 -3 -5 4 y = f (x) y = f (x - 4) y = f (x + 3)

  18. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for each graph. Click the mouse to see the answers. y a b x -3 8 3 2 -5 -11 0 y =9 - (x - 5)2 y = 9 - x2 y =9 - (x + 8)2

  19. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 2 Continue with Section 3

  20. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 3 y = -f (x)Reflect in x-axis

  21. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y  y = f (x)   x In this graph every point on y = f(x) has beenreflected in the x - axis.  y = - f (x) 

  22. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for each graph. Click the mouse to see the answers. y y = x2 b y =(x - 5)2 x 5 a y = -x2

  23. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for each graph. Click the mouse to see the answers. y y = f (x) x -6 -2 b y = -f (x) a y = f (x + 6)

  24. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for each graph. Click the mouse to see the answers. y 1 0.5 0 x 90 360 180 270 -0.5 -1 y =sin x b a y =-sin x y =sin(x - 30)

  25. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 3 Continue with Section 4

  26. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 4 y = f (-x)Reflect in y-axis

  27. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y     x In this graph every point on y = f(x) has beenreflected in the y - axis.  y = f (x) y = f (-x)

  28. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for each graph. Click the mouse to see the answers. y y = f (x) y = f (-x) b x a y =-f(x)

  29. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for each graph. Click the mouse to see the answers. y 5 y = f (x) a y = f (-x) x 0 b y = f (x)- 5

  30. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for each graph. Click the mouse to see the answers. y a y = f (x) y = f (-x) x 0 y = - f (x) b

  31. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 4 Continue with Section 5

  32. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 5 y = kf (x)Stretch/compress vertically

  33. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs In this graph everyy - value of y = sinx has been doubled. y =2 sin x y  2 1.5 y =sin x  1  0.5  0 x 90 270 360 180  -0.5 In this graph everyy - value of y = sinxhas been halved.  y =½sin x -1 -1.5  -2

  34. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y = k f (x) , k  1 y y = f (x) 0 x y = k f (x) , k 1

  35. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for each graph. Click the mouse to see the answers. y 4 a y =4sin x 3 2 y =2sin x b 1 0 x -1 y =sin x -2 -3 -4

  36. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for each graph. Click the mouse to see the answers. y 3 a y =4cos x 2 y =cos x 1 0 x -1 y =½cos x b -2 -3

  37. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for each graph. Click the mouse to see the answers. y a y =1.5sin x 1 0 x b y =sin x y =0.5sin x -1

  38. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 5 Continue with Section 6

  39. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs Section 6 y = f (kx)Stretch/compress horizontally

  40. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs In this graph everyy - value = sin (doublex) y = sin 2x y   1 y =sin x   0.5   0 x 270 360 90 180  y = sin 2x° runsthrough 2 cycles in the time y = sinx°runs through 1 cycle -0.5 -1

  41. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs In this graph everyy - value = sin (halfx) y = sin ½x y   1   0.5 y =sin x   0 x 270 360 90 180  y = sin ½x° runsthrough ½ of acycle in the time y = sinx°runs through 1 cycle -0.5 -1

  42. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs y = f (2x) y = f (x) y = f (½x) y 4 cycles 2 cycles 1 cycle 1 How manycycles? How manycycles? 0 x How manycycles? -1

  43. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 1Write down an equation for this graph. Click the mouse to see the answer. y 1 y =sin x x 0 90 180 360 270 y =sin 3x -1

  44. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 2Write down an equation for this graph. Click the mouse to see the answer. y 1 y =sin x x 0 900 180 540 720 1080 360 y =sin 1/3x -1

  45. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 3Write down an equation for this graph. Click the mouse to see the answer. y y =sin x 1 x 0 540 720 180 360 -1 y =sin ½x

  46. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 4Write down an equation for this graph. Click the mouse to see the answer. y y =sin x 1 0 x 90 270 180 360 -1 y =sin 2x

  47. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 5Write down an equation for this graph. Click the mouse to see the answer. y y =cos x 1 0 x 90 270 180 360 -1 y =cos 2x

  48. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 6Write down an equation for this graph. Click the mouse to see the answer. y y =cos x 1 0 x 90 450 540 720 360 270 180 630 -1 y =cos ½x

  49. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs 7Write down an equation for each graph. Click the mouse to see the answers. y a y =3 sin x 3 y =-sin x b 2 1 0 x 90 450 540 720 360 270 180 630 -1 y =sin x -2 -3 y =sin x - 3 c

  50. Mathematics 1(Higher) Outcome 2 Associate functions and graphs PC(a) Sketch and identify related functions and graphs End of Section 6 and PC(a) Now do Sections A1 and A2 on pages15 - 17 of the Basic Skills booklet

More Related