1. Transformations of graphs To explore geometrical transformations and their effects on the graphs of functions To relate transformations with the variations in the equation of a function. Generalobjectives:

2. Youmustbeabletorecognisethegraphsof differentfunctionsandtodrawasketch withoutcalculator. constantfunction 3. identityfunction 4. absolutevaluefunction 5. quadraticfunction 6. squarerootfunction 7. cubicfunction 8. reciprocalfuntion 9. exponentialfunction 10. trigonometricfuntion 11. inversesquarefunction 12. Transformations of graphs To explore vertical and horizontal translations and their effects on the graphs of functions To relate translations with the variations in the equation of a function. TRANSLATIONS Lesson1 13. Based on the graph of f(x), draw the graph of f(x)+3 14. Whatwillthegraphoff(x)2be? Verticaltranslation.ggb 15. Based on the graph of f(x), draw the graph of f(x)1 y=f(x) 16. This is the graph of y=f(x) .Sketch the graph of f(x)4 y=f(x) 17. Conclusions: If y=f(x) y=f(x)+c translates vertically the graph of y=f(x),cunits. If it moves upwards. If it moves downwards. c>0 c0 translates horizontally the graph of y=f(x), b units to the right. translates horizontally the graph of y=f(x), b units to the left. translation vector: translation vector: 25. Exercise1: Sketchthegraphof:f(x)2f(x3) f(x) 26. Exercise2: Sketchthegraphofthefunction Hence,sketchthegraphof 27. Exercise3: Sketchthegraphof Sketchthegraphof Findg(x)initssimplestform. 28. Exercise4: Sketchthegraphof andindicateclearlyanyasymptote. Sketchthegraphof andindicateclearlyanyasymptote. 29. Exercise5: Sketchthegraphof andindicateclearlyanyasymptote. Sketchthegraphof andindicateclearlyanyasymptote. 30. Thefunction istranslatedandits vertexisnowthepoint(2,3). Whattranslationswereappliedtofunctionf? Willtheorderinwhichyouapplythetranslations affectthefinalresult? Givetheformulaofthenewfunction. 31. Lesson2 Given sketchthegraphsofthefollowingfunctionsonthe samesetofaxes. 32. Transformations of graphs To explore stretches and reflections and their effects on the graphs of functions To relate stretches and reflections with the variations in the equation of a function. STRETCH Lesson2 REFLECTIONS 33. What is the effect on the graph of that will produce if y=f(x) y=af(x)? "a" Set up your GDC in "degrees". Prepare domain : With your calculator , plot the graphs of 34. y=sinx Verticalstretch.ggb 35. Verify your conclusion for the graphs of 36. Conclusions: y=af(x) y=f(x)If a>1 stretches vertically the graph of y=f(x), scale factor: stretches vertically the graph of y=f(x), scale factor: a y=f(x) 1 a 1 a 37. Use your calculator to draw the graph of , for On the same grid draw What effect produces the "2" of f(2x) on the graph of f(x)? 38. y=sin(2x) horizontalstretch,scalefactor y=sinx y=sin(2x) Now , draw and Horizontalstretch.ggb 39. y=sin(x) horizontalstretch,scalefactor2 y=sinx y=sin(x) 40. Conclusions: y=f(x)If a>1 y=f(ax) stretches horizontally the graph of y=f(x), scale factor: 1 a y=f(x)1 a stretches horizontally the graph of y=f(x), scale factor: a Apoint(x,y)onthegraphofy=f(x)is transformedtothepoint inthegraphof y=f(ax) 41. Exercise1: Thefunctionfisdefinedby SketchthefunctionwiththehelpofyourGDC. Describethegeometrictransformationthat willapplytothegraphoff. 42. Use your calculator to draw the graphs of and What geometrical transformation does -f(x) represent? 43. Based on the graph of y=f(x), draw the graph ofy=f(x). 44. Write down the equations of both lines . 45. Reflect the following function about the y-axis. 46. Complete: g(2)=f(.....) g(1)=f(.....) g(1)=f(.....) g(2)=f(.....) g(x)=f(.......) y=f(x)y=g(x) 47. Conclusions: y=f(x) y=f(x) y=f(x)If reflects the graph of y=f(x), about the x-axis. reflects the graph ofy=f(x), about the y-axis. 48. f(x) f(x2) f(x)+3 2f(x) Match graphs and formulae: 49. f(x) f(x)+a bf(x)+c bf(x) f(x+a) 50. y=f(x) y=af(x) y=f(ax) 51. Translations vertical translation horizontal translation Stretchs vertical stretch (a) horizontal stretch () Reflections reflection x-axis reflection y-axis c ALibraryOfFunctionsWithTransformations.nbp 52. To revise this topic at home: http://enlvm.usu.edu/ma/nav/activity.jsp?sid=__shared&cid=emready@trfns&lid=136 http://archives.math.utk.edu/visual.calculus/0/shifting.7/index.html When you feel ready, self-assessment: 53. SolveBookpage86 Exercise3A Exercises 1)c)d) 2)c)d) 3)b) 4)c)d) 5)c)d) 8)9)10)11)12)13) 54. Attachments Verticaltranslationexponential.ggb Horizontaltranslationquadratic.ggb ALibraryOfFunctionsWithTransformations.nbp Horizontalstretch.ggb Verticaltranslation.ggb Horizontaltranslation.ggb Verticalstretch.ggb