of graphs
Lecture slides prepared by: Viktor Ten
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Basic transformations of graphs презентация
Содержание
- 1. Basic transformations of graphs
- 2. Lecture overview: learning outcomes At the end
- 3. 1.5.1 : Sketch the graph of cubic
- 4. Foundation Year Program 2017-18
- 5. Foundation Year Program 2017-18
- 6. Foundation Year Program 2017-18 2A
- 7. Foundation Year Program 2017-18
- 8. Foundation Year Program 2017-18 Transformations We will
- 9. 1.5.2. Horizontal translation Foundation Year Program 2017-18
- 10. 1.5.3. Vertical translation Foundation Year Program 2017-18
- 11. Foundation Year Program 2017-18
- 12. Foundation Year Program 2017-18
- 13. Foundation Year Program 2017-18
- 14. Foundation Year Program 2017-18
- 15. 1.5.4. Vertical stretch Foundation Year Program 2017-18
- 16. 1.5.5 Horizontal stretch Foundation Year Program 2017-18
- 17. Foundation Year Program 2017-18
- 18. Foundation Year Program 2017-18
- 19. Foundation Year Program 2017-18
- 20. 1.5.6 Simple combined transformations Foundation Year Program 2017-18
- 21. Foundation Year Program 2017-18
- 22. Foundation Year Program 2017-18
- 23. Foundation Year Program 2017-18
- 24. Foundation Year Program 2017-18
- 25. Foundation Year Program 2017-18
- 26. Foundation Year Program 2017-18
- 27. Foundation Year Program 2017-18
- 28. Foundation Year Program 2017-18
- 29. In this lecture, we covered 1.5.1 Sketch
- 30. Next lecture 1.6 Simultaneous equations Foundation Year Program 2017-18
- 31. Material in some of these slides has
Lecture overview: learning outcomes At the end of this lecture, you should be able to: 1.5.1 Sketch the graph of a cubic function given in factorized form. 1.5.2 Apply a horizontal
Слайд 1Foundation Year Program
2017-18
NUFYP Mathematics & Computing Science
Pre-Calculus course
1.5 Basic transformations
Слайд 2Lecture overview: learning outcomes
At the end of this lecture, you should
be able to:
1.5.1 Sketch the graph of a cubic function given in factorized form.
1.5.2 Apply a horizontal translation to a given curve.
1.5.3 Apply a vertical translation to a given curve.
1.5.4 Apply a vertical stretch to a given curve.
1.5.5 Apply a horizontal stretch to a given curve.
1.5.6 Apply simple combined transformations to a given curve.
1.5.1 Sketch the graph of a cubic function given in factorized form.
1.5.2 Apply a horizontal translation to a given curve.
1.5.3 Apply a vertical translation to a given curve.
1.5.4 Apply a vertical stretch to a given curve.
1.5.5 Apply a horizontal stretch to a given curve.
1.5.6 Apply simple combined transformations to a given curve.
Foundation Year Program
2017-18
Слайд 31.5.1 : Sketch the graph of cubic function given in factorized
form.
Foundation Year Program
2017-18
Слайд 8Foundation Year Program
2017-18
Transformations
We will now consider four elementary transformations and some
simple combined transformations.
f(x) → f(x+a) Translation (x-axis)
f(x) → f(x)+a Translation (y-axis)
f(x) → f(ax) Scaling (stretching)(x-axis)
f(x) → af(x) Scaling (stretching)(y-axis)
f(x) → f(x+a) Translation (x-axis)
f(x) → f(x)+a Translation (y-axis)
f(x) → f(ax) Scaling (stretching)(x-axis)
f(x) → af(x) Scaling (stretching)(y-axis)
Слайд 91.5.2. Horizontal translation
Foundation Year Program
2017-18
f(x) → f(x + a)
Shape is unchanged.
Moves
to the left if a>0.
Moves to the right if a<0.
Moves to the right if a<0.
h(x) =(x+2)2 - 4
f(x) = x2 - 4
g(x) =(x-2)2 - 4
Слайд 101.5.3. Vertical translation
Foundation Year Program
2017-18
Shape is unchanged.
Moves upwards if a>0.
Moves downwards
if a<0.
h(x) = x2 - 8
g(x) = x2
f(x) = x2 - 4
Слайд 151.5.4. Vertical stretch
Foundation Year Program
2017-18
Roots unchanged
Axis of symmetry unchanged
Intercept at (0,
c) is transformed to (0, ac)
If a < 0, the branches of transformed curve are reoriented from upward to downward or vice versa from original.
If a < 0, the branches of transformed curve are reoriented from upward to downward or vice versa from original.
f(x) = x2 - 4
h(x) = -0.5(x2 – 4)
g(x) = 2(x2 – 4)
Слайд 161.5.5 Horizontal stretch
Foundation Year Program
2017-18
f(x) = x2 - 4
h(x) = (0.5x)2
- 4
Even power. Location of roots changes if |a|≠ 1. Axis of symmetry unchanged.
g(x) = (2x)2 - 4
f(x) = x3 – 3x2 – x + 2
g(x) = (1.2x)3 – 3(1.2x)2 –(1.2x) + 2
h(x) = (0.8x)3 – 3(0.8x)2 –(0.8x) + 2
Odd power.
Слайд 29In this lecture, we covered
1.5.1 Sketch the graph of a cubic
function given in factorized form.
1.5.2 Apply a horizontal translation to a given curve.
1.5.3 Apply a vertical translation to a given curve.
1.5.4 Apply a vertical stretch to a given curve.
1.5.5 Apply a horizontal stretch to a given curve.
1.5.6 Apply simple combined transformations to a given curve.
1.5.2 Apply a horizontal translation to a given curve.
1.5.3 Apply a vertical translation to a given curve.
1.5.4 Apply a vertical stretch to a given curve.
1.5.5 Apply a horizontal stretch to a given curve.
1.5.6 Apply simple combined transformations to a given curve.
Foundation Year Program
2017-18
Слайд 31Material in some of these slides has been reproduced from:
Attwood,
G., Macpherson, A., Moran, B., Petran, J., Pledger, K., Staley, G. and Wilkins, D. (2008), Edexcel AS and A Level Modular Mathematics series C1, Pearson, Harlow, UK.
Attwood, G., Macpherson, A., Moran, B., Petran, J., Pledger, K., Staley, G. and Wilkins, D. (2008), Edexcel AS and A Level Modular Mathematics series C3, Pearson, Harlow, UK.
Attwood, G., Macpherson, A., Moran, B., Petran, J., Pledger, K., Staley, G. and Wilkins, D. (2008), Edexcel AS and A Level Modular Mathematics series C3, Pearson, Harlow, UK.
Foundation Year Program
2017-18
