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Functions 1

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Functions 1

  1. 1. 1Ago 27­06:48 p.m.Interval notationStarter:
  2. 2. 2Ago 27­06:48 p.m.
  3. 3. 3Ago 27­06:48 p.m.By the end of the lesson you will be able to:• Distinguish between relations and functions.• Recognise the domain and range of a function     from its graph or/and its formula.• Use  GDC to draw graphs of functions.• Manipulate function notation.
  4. 4. 4Ago 27­06:48 p.m.RelationsA relation is any set of points on the cartesian plane.A relation is often expressed as an equationconnecting two variables  .
  5. 5. 5Ago 27­06:48 p.m.The length side of a square is x. Write the area of the square, A, in terms of x.A group of friends rents a car for their holidays. They have to pay a fixed cost of 350$ plus $120 per day. Let C be the cost of renting the car and d the number of days the car is rented. Write C in terms of d.The value of a car depreciates in such a way that when it is t years old,  its value V is given by V=12000e­0.6t. (a) Find the value of the car after 4 years.(b) How long does it take for the car to be worth 6000?A(x) = x2C(d) = 350+120d
  6. 6. 6Ago 27­06:48 p.m.A(x) = x2C(d) = 350+120d V(t) =12000e­0.6tA function is a relation in which to each value of xcorresponds one and only one value of y.FunctionsA(x) = x2 independent variable? dependent variable?C(d) = 350+120dindependent variable?independent variable?V(t) =12000e­0.6t dependent variable? dependent variable?
  7. 7. 7Ago 27­06:48 p.m.A(x) = x2V(t) =12000e­0.6tFunction notationFind  A(3)Find  x  if A(x) = 100What is the meaning of V(4) ?What is the image  of t=4 ?
  8. 8. 8Ago 27­06:48 p.m.Functions can also be given by graphsnot a functionnot a functionWhich of these graphs represent functions? function function functionvertical line test.exe
  9. 9. 9Ago 27­06:48 p.m. functio function function for all real numbers but zero functionhttp://www.univie.ac.at/future.media/moe/tests/fun1/grongr.html
  10. 10. 10Ago 27­06:48 p.m.The domain of a function is the set of permissiblevalues that x may have.A(x) = x2Domain=Use your GDC to plot the graph of A.Range =The range of a function is the set ofall the images( y ).
  11. 11. 11Ago 27­06:48 p.m.The domain of a function is the set of permissiblevalues that x may have.The range of a function is the set of all the images( y ).domainrange
  12. 12. 12Ago 27­06:48 p.m.State the domain and range of the function :
  13. 13. 13Ago 27­06:48 p.m.State the domain and range of the function :
  14. 14. 14Ago 27­06:48 p.m.State the domain and range of the function :
  15. 15. 15Ago 27­06:48 p.m.State the domain and range of the function :
  16. 16. 16Ago 27­06:48 p.m.State the domain and range of the function :
  17. 17. 17Ago 27­06:48 p.m.y = x2 ­ 3x + 5y = 3x + 5 y = x5 ­ 3x3    Polynomial functions.The domain of any polynomial function is the set of realnumbers:
  18. 18. 18Ago 27­06:48 p.m.State the domain of the function :Draw the graph of this function with your GDC.Is there any value of x for which you cant calculate thevalue of y ?Domain:
  19. 19. 19Ago 27­06:48 p.m.What is the range of this function?
  20. 20. 20Ago 27­06:48 p.m.State the domain of the function:Draw the graph of this function with your GDC.Domain:Is there any value of x for which you cant calculate thevalue of y ?
  21. 21. 21Ago 27­06:48 p.m.This function is called the reciprocal function. Its graph is a hyperbola.What is the range of this function?
  22. 22. 22Ago 27­06:48 p.m.Find the domain and range of:Domain:Draw the graph of this function with your GDC.Is there any value of x for which you cant calculate thevalue of y ?
  23. 23. 23Ago 27­06:48 p.m.What is the range of this function?
  24. 24. 24Ago 27­06:48 p.m.C  Which graph is not a function?yxxyxyxyD  xy
  25. 25. 25Ago 27­06:48 p.m.A  B  C  D  Which graph is  a function? A  B  C  D  
  26. 26. Attachmentsvertical line test.exe

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